1st law of thermodynamics experiment

15.1 The First Law of Thermodynamics

Learning objectives.

By the end of this section, you will be able to:

• Define the first law of thermodynamics.
• Describe how conservation of energy relates to the first law of thermodynamics.
• Identify instances of the first law of thermodynamics working in everyday situations, including biological metabolism.
• Calculate changes in the internal energy of a system, after accounting for heat transfer and work done.

If we are interested in how heat transfer is converted into doing work, then the conservation of energy principle is important. The first law of thermodynamics applies the conservation of energy principle to systems where heat transfer and doing work are the methods of transferring energy into and out of the system. The first law of thermodynamics states that the change in internal energy of a system equals the net heat transfer into the system minus the net work done by the system. In equation form, the first law of thermodynamics is

Here Δ E int Δ E int is the change in internal energy E int E int of the system. Q Q is the net heat transferred into the system —that is, Q Q is the sum of all heat transfer into and out of the system. W W is the net work done by the system —that is, W W is the sum of all work done on or by the system. We use the following sign conventions: if Q Q is positive, then there is a net heat transfer into the system; if W W is positive, then there is net work done by the system. So positive Q Q adds energy to the system and positive W W takes energy from the system. Thus Δ E int = Q − W Δ E int = Q − W . Note also that if more heat transfer into the system occurs than work done, the difference is stored as internal energy. Heat engines are a good example of this—heat transfer into them takes place so that they can do work. (See Figure 15.3 .) We will now examine Q Q , W W , and Δ E int Δ E int further.

Making Connections: Law of Thermodynamics and Law of Conservation of Energy

The first law of thermodynamics is actually the law of conservation of energy stated in a form most useful in thermodynamics. The first law gives the relationship between heat transfer, work done, and the change in internal energy of a system.

Heat Q and Work W

Heat transfer ( Q Q ) and doing work ( W W ) are the two everyday means of bringing energy into or taking energy out of a system. The processes are quite different. Heat transfer, a less organized process, is driven by temperature differences. Work, a quite organized process, involves a macroscopic force exerted through a distance. Nevertheless, heat and work can produce identical results.For example, both can cause a temperature increase. Heat transfer into a system, such as when the Sun warms the air in a bicycle tire, can increase its temperature, and so can work done on the system, as when the bicyclist pumps air into the tire. Once the temperature increase has occurred, it is impossible to tell whether it was caused by heat transfer or by doing work. This uncertainty is an important point. Heat transfer and work are both energy in transit—neither is stored as such in a system. However, both can change the internal energy E int E int of a system. Internal energy is a form of energy completely different from either heat or work.

Internal Energy E int

We can think about the internal energy of a system in two different but consistent ways. The first is the atomic and molecular view, which examines the system on the atomic and molecular scale. The internal energy E int E int of a system is the sum of the kinetic and potential energies of its atoms and molecules. Recall that kinetic plus potential energy is called mechanical energy. Thus internal energy is the sum of atomic and molecular mechanical energy. Because it is impossible to keep track of all individual atoms and molecules, we must deal with averages and distributions. A second way to view the internal energy of a system is in terms of its macroscopic characteristics, which are very similar to atomic and molecular average values.

Macroscopically, we define the change in internal energy Δ E int Δ E int to be that given by the first law of thermodynamics:

Many detailed experiments have verified that Δ E int = Q − W Δ E int = Q − W , where Δ E int Δ E int is the change in total kinetic and potential energy of all atoms and molecules in a system. It has also been determined experimentally that the internal energy E int E int of a system depends only on the state of the system and not how it reached that state . More specifically, E int E int is found to be a function of a few macroscopic quantities (pressure, volume, and temperature, for example), independent of past history such as whether there has been heat transfer or work done. This independence means that if we know the state of a system, we can calculate changes in its internal energy E int E int from a few macroscopic variables.

Making Connections: Macroscopic and Microscopic

In thermodynamics, we often use the macroscopic picture when making calculations of how a system behaves, while the atomic and molecular picture gives underlying explanations in terms of averages and distributions. We shall see this again in later sections of this chapter. For example, in the topic of entropy, calculations will be made using the atomic and molecular view.

To get a better idea of how to think about the internal energy of a system, let us examine a system going from State 1 to State 2. The system has internal energy E int1 E int1 in State 1, and it has internal energy E int2 E int2 in State 2, no matter how it got to either state. So the change in internal energy Δ E int = E int2 − E int1 Δ E int = E int2 − E int1 is independent of what caused the change. In other words, Δ E int Δ E int is independent of path . By path, we mean the method of getting from the starting point to the ending point. Why is this independence important? Note that Δ E int = Q − W Δ E int = Q − W . Both Q Q and W W depend on path , but Δ E int Δ E int does not. This path independence means that internal energy E int E int is easier to consider than either heat transfer or work done.

Example 15.1

Calculating change in internal energy: the same change in e int e int is produced by two different processes.

(a) Suppose there is heat transfer of 40.00 J to a system, while the system does 10.00 J of work. Later, there is heat transfer of 25.00 J out of the system while 4.00 J of work is done on the system. What is the net change in internal energy of the system?

(b) What is the change in internal energy of a system when a total of 150.00 J of heat transfer occurs out of (from) the system and 159.00 J of work is done on the system? (See Figure 15.4 ).

In part (a), we must first find the net heat transfer and net work done from the given information. Then the first law of thermodynamics ( Δ E int = Q − W ) ( Δ E int = Q − W ) can be used to find the change in internal energy. In part (b), the net heat transfer and work done are given, so the equation can be used directly.

Solution for (a)

The net heat transfer is the heat transfer into the system minus the heat transfer out of the system, or

Similarly, the total work is the work done by the system minus the work done on the system, or

Thus the change in internal energy is given by the first law of thermodynamics:

We can also find the change in internal energy for each of the two steps. First, consider 40.00 J of heat transfer in and 10.00 J of work out, or

Now consider 25.00 J of heat transfer out and 4.00 J of work in, or

The total change is the sum of these two steps, or

Discussion on (a)

No matter whether you look at the overall process or break it into steps, the change in internal energy is the same.

Solution for (b)

Here the net heat transfer and total work are given directly to be Q = – 150.00 J Q = – 150.00 J and W = – 159.00 J W = – 159.00 J , so that

Discussion on (b)

A very different process in part (b) produces the same 9.00-J change in internal energy as in part (a). Note that the change in the system in both parts is related to Δ E int Δ E int and not to the individual Q Q s or W W s involved. The system ends up in the same state in both (a) and (b). Parts (a) and (b) present two different paths for the system to follow between the same starting and ending points, and the change in internal energy for each is the same—it is independent of path.

Human Metabolism and the First Law of Thermodynamics

Human metabolism is the conversion of food into heat transfer, work, and stored fat. Metabolism is an interesting example of the first law of thermodynamics in action. We now take another look at these topics via the first law of thermodynamics. Considering the body as the system of interest, we can use the first law to examine heat transfer, doing work, and internal energy in activities ranging from sleep to heavy exercise. What are some of the major characteristics of heat transfer, doing work, and energy in the body? For one, body temperature is normally kept constant by heat transfer to the surroundings. This means Q Q is negative. Another fact is that the body usually does work on the outside world. This means W W is positive. In such situations, then, the body loses internal energy, since Δ E int = Q − W Δ E int = Q − W is negative.

Now consider the effects of eating. Eating increases the internal energy of the body by adding chemical potential energy (this is an unromantic view of a good steak). The body metabolizes all the food we consume. Basically, metabolism is an oxidation process in which the chemical potential energy of food is released. This implies that food input is in the form of work. Food energy is reported in a special unit, known as the Calorie. This energy is measured by burning food in a calorimeter, which is how the units are determined.

In chemistry and biochemistry, one calorie (spelled with a lowercase c) is defined as the energy (or heat transfer) required to raise the temperature of one gram of pure water by one degree Celsius. Nutritionists and weight-watchers tend to use the dietary calorie, which is frequently called a Calorie (spelled with a capital C). One food Calorie is the energy needed to raise the temperature of one kilogram of water by one degree Celsius. This means that one dietary Calorie is equal to one kilocalorie for the chemist, and one must be careful to avoid confusion between the two.

Again, consider the internal energy the body has lost. There are three places this internal energy can go—to heat transfer, to doing work, and to stored fat (a tiny fraction also goes to cell repair and growth). Heat transfer and doing work take internal energy out of the body, and food puts it back. If you eat just the right amount of food, then your average internal energy remains constant. Whatever you lose to heat transfer and doing work is replaced by food, so that, in the long run, Δ E int = 0 Δ E int = 0 . If you overeat repeatedly, then Δ E int Δ E int is always positive, and your body stores this extra internal energy as fat. The reverse is true if you eat too little. If Δ E int Δ E int is negative for a few days, then the body metabolizes its own fat to maintain body temperature and do work that takes energy from the body. This process is how dieting produces weight loss.

Life is not always this simple, as any dieter knows. The body stores fat or metabolizes it only if energy intake changes for a period of several days. Once you have been on a major diet, the next one is less successful because your body alters the way it responds to low energy intake. Your basal metabolic rate (BMR) is the rate at which food is converted into heat transfer and work done while the body is at complete rest. The body adjusts its basal metabolic rate to partially compensate for over-eating or under-eating. The body will decrease the metabolic rate rather than eliminate its own fat to replace lost food intake. You will chill more easily and feel less energetic as a result of the lower metabolic rate, and you will not lose weight as fast as before. Exercise helps to lose weight, because it produces both heat transfer from your body and work, and raises your metabolic rate even when you are at rest. Weight loss is also aided by the quite low efficiency of the body in converting internal energy to work, so that the loss of internal energy resulting from doing work is much greater than the work done.It should be noted, however, that living systems are not in thermal equilibrium.

The body provides us with an excellent indication that many thermodynamic processes are irreversible . An irreversible process can go in one direction but not the reverse, under a given set of conditions. For example, although body fat can be converted to do work and produce heat transfer, work done on the body and heat transfer into it cannot be converted to body fat. Otherwise, we could skip lunch by sunning ourselves or by walking down stairs. Another example of an irreversible thermodynamic process is photosynthesis. This process is the intake of one form of energy—light—by plants and its conversion to chemical potential energy. Both applications of the first law of thermodynamics are illustrated in Figure 15.5 . One great advantage of conservation laws such as the first law of thermodynamics is that they accurately describe the beginning and ending points of complex processes, such as metabolism and photosynthesis, without regard to the complications in between. Table 15.1 presents a summary of terms relevant to the first law of thermodynamics.

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Thermodynamics

The first law of thermodynamics, learning objectives.

By the end of this section, you will be able to:

• Define the first law of thermodynamics.
• Describe how conservation of energy relates to the first law of thermodynamics.
• Identify instances of the first law of thermodynamics working in everyday situations, including biological metabolism.
• Calculate changes in the internal energy of a system, after accounting for heat transfer and work done.

Figure 1. This boiling tea kettle represents energy in motion. The water in the kettle is turning to water vapor because heat is being transferred from the stove to the kettle. As the entire system gets hotter, work is done—from the evaporation of the water to the whistling of the kettle. (credit: Gina Hamilton)

If we are interested in how heat transfer is converted into doing work, then the conservation of energy principle is important. The first law of thermodynamics applies the conservation of energy principle to systems where heat transfer and doing work are the methods of transferring energy into and out of the system. The first law of thermodynamics states that the change in internal energy of a system equals the net heat transfer into the system minus the net work done by the system. In equation form, the first law of thermodynamics is Δ U  =  Q  −  W .

Here Δ U is the change in internal energy U of the system. Q is the net heat transferred into the system —that is, Q is the sum of all heat transfer into and out of the system. W is the net work done by the system —that is, W is the sum of all work done on or by the system. We use the following sign conventions: if Q is positive, then there is a net heat transfer into the system; if W is positive, then there is net work done by the system. So positive Q adds energy to the system and positive W takes energy from the system. Thus Δ U  =  Q  −  W . Note also that if more heat transfer into the system occurs than work done, the difference is stored as internal energy. Heat engines are a good example of this—heat transfer into them takes place so that they can do work. (See Figure 2.) We will now examine Q , W , and Δ U further.

Figure 2. The first law of thermodynamics is the conservation-of-energy principle stated for a system where heat and work are the methods of transferring energy for a system in thermal equilibrium. Q represents the net heat transfer—it is the sum of all heat transfers into and out of the system. Q is positive for net heat transfer into the system. W is the total work done on and by the system. W is positive when more work is done by the system than on it. The change in the internal energy of the system, Δ U , is related to heat and work by the first law of thermodynamics, Δ U = Q − W .

Making Connections: Law of Thermodynamics and Law of Conservation of Energy

The first law of thermodynamics is actually the law of conservation of energy stated in a form most useful in thermodynamics. The first law gives the relationship between heat transfer, work done, and the change in internal energy of a system.

Heat Q and Work W

Heat transfer ( Q ) and doing work ( W ) are the two everyday means of bringing energy into or taking energy out of a system. The processes are quite different. Heat transfer, a less organized process, is driven by temperature differences. Work, a quite organized process, involves a macroscopic force exerted through a distance. Nevertheless, heat and work can produce identical results.For example, both can cause a temperature increase. Heat transfer into a system, such as when the Sun warms the air in a bicycle tire, can increase its temperature, and so can work done on the system, as when the bicyclist pumps air into the tire. Once the temperature increase has occurred, it is impossible to tell whether it was caused by heat transfer or by doing work. This uncertainty is an important point. Heat transfer and work are both energy in transit—neither is stored as such in a system. However, both can change the internal energy U of a system. Internal energy is a form of energy completely different from either heat or work.

Internal Energy U

We can think about the internal energy of a system in two different but consistent ways. The first is the atomic and molecular view, which examines the system on the atomic and molecular scale. The internal energy U of a system is the sum of the kinetic and potential energies of its atoms and molecules. Recall that kinetic plus potential energy is called mechanical energy. Thus internal energy is the sum of atomic and molecular mechanical energy. Because it is impossible to keep track of all individual atoms and molecules, we must deal with averages and distributions. A second way to view the internal energy of a system is in terms of its macroscopic characteristics, which are very similar to atomic and molecular average values.

Macroscopically, we define the change in internal energy Δ U to be that given by the first law of thermodynamics: Δ U  =  Q −  W .

Many detailed experiments have verified that Δ U  =  Q  −  W , where Δ U is the change in total kinetic and potential energy of all atoms and molecules in a system. It has also been determined experimentally that the internal energy U of a system depends only on the state of the system and not how it reached that state . More specifically, U is found to be a function of a few macroscopic quantities (pressure, volume, and temperature, for example), independent of past history such as whether there has been heat transfer or work done. This independence means that if we know the state of a system, we can calculate changes in its internal energy U from a few macroscopic variables.

Making Connections: Macroscopic and Microscopic

In thermodynamics, we often use the macroscopic picture when making calculations of how a system behaves, while the atomic and molecular picture gives underlying explanations in terms of averages and distributions. We shall see this again in later sections of this chapter. For example, in the topic of entropy, calculations will be made using the atomic and molecular view.

To get a better idea of how to think about the internal energy of a system, let us examine a system going from State 1 to State 2. The system has internal energy U 1 in State 1, and it has internal energy U 2 in State 2, no matter how it got to either state. So the change in internal energy Δ U  =  U 2  −  U 1 is independent of what caused the change. In other words, Δ U is independent of path . By path, we mean the method of getting from the starting point to the ending point. Why is this independence important? Note that Δ U  =  Q  −  W . Both Q and W depend on path , but Δ U does not. This path independence means that internal energy U is easier to consider than either heat transfer or work done.

Example 1. Calculating Change in Internal Energy: The Same Change in U is Produced by Two Different Processes

• Suppose there is heat transfer of 40.00 J to a system, while the system does 10.00 J of work. Later, there is heat transfer of 25.00 J out of the system while 4.00 J of work is done on the system. What is the net change in internal energy of the system?
• What is the change in internal energy of a system when a total of 150.00 J of heat transfer occurs out of (from) the system and 159.00 J of work is done on the system? (See Figure 3).

Figure 3. Two different processes produce the same change in a system. (a) A total of 15.00 J of heat transfer occurs into the system, while work takes out a total of 6.00 J. The change in internal energy is ΔU=Q−W=9.00 J. (b) Heat transfer removes 150.00 J from the system while work puts 159.00 J into it, producing an increase of 9.00 J in internal energy. If the system starts out in the same state in (a) and (b), it will end up in the same final state in either case—its final state is related to internal energy, not how that energy was acquired.

In part 1, we must first find the net heat transfer and net work done from the given information. Then the first law of thermodynamics (Δ U  =  Q  −  W ) can be used to find the change in internal energy. In part (b), the net heat transfer and work done are given, so the equation can be used directly.

Solution for Part 1

The net heat transfer is the heat transfer into the system minus the heat transfer out of the system, or

Q = 40.00 J − 25.00 J = 15.00 J.

Similarly, the total work is the work done by the system minus the work done on the system, or

W  = 10.00 J − 4.00 J = 6.00 J.

Thus the change in internal energy is given by the first law of thermodynamics:

Δ U  =  Q  −  W  = 15.00 J − 6.00 J = 9.00 J.

We can also find the change in internal energy for each of the two steps. First, consider 40.00 J of heat transfer in and 10.00 J of work out, or Δ U 1  =  Q 1  −  W 1  = 40.00 J − 10.00 J = 30.00 J.

Now consider 25.00 J of heat transfer out and 4.00 J of work in, or

 Δ U 2  =  Q 2  −  W 2  = –25.00 J −(−4.00 J) = –21.00 J.

The total change is the sum of these two steps, or Δ U  = Δ U 1  + Δ U 2  = 30.00 J + (−21.00 J) = 9.00 J.

Discussion on Part 1

No matter whether you look at the overall process or break it into steps, the change in internal energy is the same.

Solution for Part 2

Here the net heat transfer and total work are given directly to be Q =–150.00 J and W =–159.00 J, so that

Δ U  =  Q  –  W  = –150.00 J –(−159.00 J) = 9.00 J.

Discussion on Part 2

A very different process in part 2 produces the same 9.00-J change in internal energy as in part 1. Note that the change in the system in both parts is related to Δ U and not to the individual Q s or W s involved. The system ends up in the same state in both parts. Parts 1 and 2 present two different paths for the system to follow between the same starting and ending points, and the change in internal energy for each is the same—it is independent of path.

Human Metabolism and the First Law of Thermodynamics

Human metabolism is the conversion of food into heat transfer, work, and stored fat. Metabolism is an interesting example of the first law of thermodynamics in action. We now take another look at these topics via the first law of thermodynamics. Considering the body as the system of interest, we can use the first law to examine heat transfer, doing work, and internal energy in activities ranging from sleep to heavy exercise. What are some of the major characteristics of heat transfer, doing work, and energy in the body? For one, body temperature is normally kept constant by heat transfer to the surroundings. This means Q is negative. Another fact is that the body usually does work on the outside world. This means W is positive. In such situations, then, the body loses internal energy, since Δ U  =  Q  −  W is negative.

Now consider the effects of eating. Eating increases the internal energy of the body by adding chemical potential energy (this is an unromantic view of a good steak). The body metabolizes all the food we consume. Basically, metabolism is an oxidation process in which the chemical potential energy of food is released. This implies that food input is in the form of work. Food energy is reported in a special unit, known as the Calorie. This energy is measured by burning food in a calorimeter, which is how the units are determined.

In chemistry and biochemistry, one calorie (spelled with a lowercase c) is defined as the energy (or heat transfer) required to raise the temperature of one gram of pure water by one degree Celsius. Nutritionists and weight-watchers tend to use the dietary calorie, which is frequently called a Calorie (spelled with a capital C). One food Calorie is the energy needed to raise the temperature of one kilogram of water by one degree Celsius. This means that one dietary Calorie is equal to one kilocalorie for the chemist, and one must be careful to avoid confusion between the two.

Again, consider the internal energy the body has lost. There are three places this internal energy can go—to heat transfer, to doing work, and to stored fat (a tiny fraction also goes to cell repair and growth). Heat transfer and doing work take internal energy out of the body, and food puts it back. If you eat just the right amount of food, then your average internal energy remains constant. Whatever you lose to heat transfer and doing work is replaced by food, so that, in the long run, Δ U =0. If you overeat repeatedly, then Δ U is always positive, and your body stores this extra internal energy as fat. The reverse is true if you eat too little. If Δ U is negative for a few days, then the body metabolizes its own fat to maintain body temperature and do work that takes energy from the body. This process is how dieting produces weight loss.

Life is not always this simple, as any dieter knows. The body stores fat or metabolizes it only if energy intake changes for a period of several days. Once you have been on a major diet, the next one is less successful because your body alters the way it responds to low energy intake. Your basal metabolic rate (BMR) is the rate at which food is converted into heat transfer and work done while the body is at complete rest. The body adjusts its basal metabolic rate to partially compensate for over-eating or under-eating. The body will decrease the metabolic rate rather than eliminate its own fat to replace lost food intake. You will chill more easily and feel less energetic as a result of the lower metabolic rate, and you will not lose weight as fast as before. Exercise helps to lose weight, because it produces both heat transfer from your body and work, and raises your metabolic rate even when you are at rest. Weight loss is also aided by the quite low efficiency of the body in converting internal energy to work, so that the loss of internal energy resulting from doing work is much greater than the work done.It should be noted, however, that living systems are not in thermalequilibrium.

The body provides us with an excellent indication that many thermodynamic processes are irreversible . An irreversible process can go in one direction but not the reverse, under a given set of conditions. For example, although body fat can be converted to do work and produce heat transfer, work done on the body and heat transfer into it cannot be converted to body fat. Otherwise, we could skip lunch by sunning ourselves or by walking down stairs. Another example of an irreversible thermodynamic process is photosynthesis. This process is the intake of one form of energy—light—by plants and its conversion to chemical potential energy. Both applications of the first law of thermodynamics are illustrated in Figure 4. One great advantage of conservation laws such as the first law of thermodynamics is that they accurately describe the beginning and ending points of complex processes, such as metabolism and photosynthesis, without regard to the complications in between. Table 1 presents a summary of terms relevant to the first law of thermodynamics.

Figure 4. (a) The first law of thermodynamics applied to metabolism. Heat transferred out of the body (Q) and work done by the body (W) remove internal energy, while food intake replaces it. (Food intake may be considered as work done on the body.) (b) Plants convert part of the radiant heat transfer in sunlight to stored chemical energy, a process called photosynthesis.

Section Summary

• The first law of thermodynamics is given as Δ U  = Q −   W , where Δ U  is the change in internal energy of a system, Q  is the net heat transfer (the sum of all heat transfer into and out of the system), and W  is the net work done (the sum of all work done on or by the system).
• Both Q  and W  are energy in transit; only Δ U  represents an independent quantity capable of being stored.
• The internal energy U  of a system depends only on the state of the system and not how it reached that state.
• Metabolism of living organisms, and photosynthesis of plants, are specialized types of heat transfer, doing work, and internal energy of systems.

Conceptual Questions

• Describe the photo of the tea kettle at the beginning of this section in terms of heat transfer, work done, and internal energy. How is heat being transferred? What is the work done and what is doing it? How does the kettle maintain its internal energy?
• The first law of thermodynamics and the conservation of energy, as discussed in Conservation of Energy , are clearly related. How do they differ in the types of energy considered?
• Heat transfer Q  and work done W  are always energy in transit, whereas internal energy U  is energy stored in a system. Give an example of each type of energy, and state specifically how it is either in transit or resides in a system.
• How do heat transfer and internal energy differ? In particular, which can be stored as such in a system and which cannot?
• If you run down some stairs and stop, what happens to your kinetic energy and your initial gravitational potential energy?
• Give an explanation of how food energy (calories) can be viewed as molecular potential energy (consistent with the atomic and molecular definition of internal energy).
• Identify the type of energy transferred to your body in each of the following as either internal energy, heat transfer, or doing work: (a) basking in sunlight; (b) eating food; (c) riding an elevator to a higher floor.

Problems & Exercises

• What is the change in internal energy of a car if you put 12.0 gal of gasoline into its tank? The energy content of gasoline is 1.3 × 10 8 J/gal. All other factors, such as the car’s temperature, are constant.
• How much heat transfer occurs from a system, if its internal energy decreased by 150 J while it was doing 30.0 J of work?
• A system does 1.80 × 10 8 J of work while 7.50 × 10 8 J of heat transfer occurs to the environment. What is the change in internal energy of the system assuming no other changes (such as in temperature or by the addition of fuel)?
• What is the change in internal energy of a system which does 4.50 × 10 5 J of work while 3.00 × 10 6 J of heat transfer occurs into the system, and 8.00 × 10 6 J of heat transfer occurs to the environment?
• Suppose a woman does 500 J of work and 9500 J of heat transfer occurs into the environment in the process. (a) What is the decrease in her internal energy, assuming no change in temperature or consumption of food? (That is, there is no other energy transfer.) (b) What is her efficiency?
• (a) How much food energy will a man metabolize in the process of doing 35.0 kJ of work with an efficiency of 5.00%? (b) How much heat transfer occurs to the environment to keep his temperature constant?
• (a) What is the average metabolic rate in watts of a man who metabolizes 10,500 kJ of food energy in one day? (b) What is the maximum amount of work in joules he can do without breaking down fat, assuming a maximum efficiency of 20.0%? (c) Compare his work output with the daily output of a 187-W (0.250-horsepower) motor.
• (a) How long will the energy in a 1470-kJ (350-kcal) cup of yogurt last in a woman doing work at the rate of 150 W with an efficiency of 20.0% (such as in leisurely climbing stairs)? (b) Does the time found in part (a) imply that it is easy to consume more food energy than you can reasonably expect to work off with exercise?
• (a) A woman climbing the Washington Monument metabolizes 6.00 × 10 2 kJ of food energy. If her efficiency is 18.0%, how much heat transfer occurs to the environment to keep her temperature constant? (b) Discuss the amount of heat transfer found in (a). Is it consistent with the fact that you quickly warm up when exercising?

first law of thermodynamics:  states that the change in internal energy of a system equals the net heat transfer into the system minus the net work done by the system

internal energy:  the sum of the kinetic and potential energies of a system’s atoms and molecules

human metabolism:  conversion of food into heat transfer, work, and stored fat

Selected Solutions to Problems & Exercises

1. 1.6 × 10 9 J

3. −9.30 × 10 8 J

5. (a) −1.0 × 10 4 J , or −2.39 kcal; (b) 5.00%

7. (a) 122 W; (b) 2.10 × 10 6 J; (c) Work done by the motor is 1.61 × 10 7 J; thus the motor produces 7.67 times the work done by the man

9. (a) 492 kJ; (b) This amount of heat is consistent with the fact that you warm quickly when exercising. Since the body is inefficient, the excess heat produced must be dissipated through sweating, breathing, etc.

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Physics archive

Course: physics archive   >   unit 10.

• Macrostates and microstates
• Quasistatic and reversible processes

First law of thermodynamics / internal energy

• More on internal energy
• What is the first law of thermodynamics?
• Work from expansion
• PV-diagrams and expansion work
• What are PV diagrams?
• Proof: U = (3/2)PV or U = (3/2)nRT
• Work done by isothermic process
• Carnot cycle and Carnot engine
• Proof: Volume ratios in a Carnot cycle
• Proof: S (or entropy) is a valid state variable
• Thermodynamic entropy definition clarification
• Reconciling thermodynamic and state definitions of entropy
• Entropy intuition
• Maxwell's demon
• More on entropy
• Efficiency of a Carnot engine
• Carnot efficiency 2: Reversing the cycle
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Video transcript

Wolfram Demonstrations Project

Joule's experiment and the first law of thermodynamics.

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Contributed by: Anping Zeng   (June 2015) Open content licensed under CC BY-NC-SA

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Anping Zeng "Joule's Experiment and the First Law of Thermodynamics" http://demonstrations.wolfram.com/JoulesExperimentAndTheFirstLawOfThermodynamics/ Wolfram Demonstrations Project Published: June 10 2015

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First Law Of Thermodynamics

The First Law of Thermodynamics states that heat is a form of energy, and thermodynamic processes are therefore subject to the principle of conservation of energy. This means that heat energy cannot be created or destroyed. It can, however, be transferred from one location to another and converted to and from other forms of energy.

Introducing State Variables

Thermodynamic state variables are the macroscopic quantities that determine a system’s thermodynamic equilibrium state. A system not in equilibrium cannot be described by state variables. State variables can further be classified as intensive or extensive variables. Intensive variables are independent of the dimensions of the system like pressure and temperature, while extensive variables depend on dimensions of the system like volume, mass, internal energy etc.

Explaining the first law of thermodynamics

The first law of thermodynamics relates to heat, internal energy, and work.

The first law of thermodynamics, also known as the law of conservation of energy, states that energy can neither be created nor destroyed, but it can be changed from one form to another.

It can be represented mathematically as

• ΔQ is the heat given or lost
• ΔU is the change in internal energy
• W is the work done

We can also represent the above equation as follows,

So we can infer from the above equation that the quantity (ΔQ – W) is independent of the path taken to change the state. Further, we can say that internal energy increases when the heat is given to the system and vice versa.

Sign Conventions

The table below shows the appropriate sign conventions for all three quantities under different conditions:

Recommended Video

First Law of Thermodynamics Solved Examples

1. Calculate the change in the system’s internal energy if 3000 J of heat is added to a system and a work of 2500 J is done.

Solution: The following sign conventions are followed in the numerical: Solution: The following sign conventions are followed in the numerical:

• Q is positive as heat is added to the system
• W is positive if work is done on the system

Hence, the change in internal energy is given as: \(\begin{array}{l}\Delta U=3000-2500\end{array} \) \(\begin{array}{l}\Delta U=500\end{array} \) The internal energy of the system is 500 J.

2. What is the change in the internal energy of the system if 2000 J of heat leaves the system and 2500 J of work is done on the system? Solution: The change in the internal energy of the system can be identified using the formula:

Substituting the values in the following equation, we get

ΔU = -2000-(-3000)

ΔU = -2000+3000

ΔU = 1000 Joule

Internal energy increases by 4500 Joules.

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first law of thermodynamics

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first law of thermodynamics , thermodynamic relation stating that, within an isolated system, the total energy of the system is constant, even if energy has been converted from one form to another. This law is another way of stating the law of conservation of energy . It is one of four relations underlying thermodynamics , the branch of physics concerning heat , work , temperature , and energy.

The first law of thermodynamics is put into action by considering the flow of energy across the boundary separating a system from its surroundings. Consider the classic example of a gas enclosed in a cylinder with a movable piston . The walls of the cylinder act as the boundary separating the gas inside from the world outside, and the movable piston provides a mechanism for the gas to do work by expanding against the force holding the piston (assumed frictionless) in place. If the gas does work W as it expands, and/or absorbs heat Q from its surroundings through the walls of the cylinder, then this corresponds to a net flow of energy W − Q across the boundary to the surroundings. In order to conserve the total energy U , there must be a counterbalancing change Δ U = Q − W in the internal energy of the gas. The first law provides a kind of strict energy accounting system in which the change in the energy account (Δ U ) equals the difference between deposits ( Q ) and withdrawals ( W ).

There is an important distinction between the quantity Δ U and the related energy quantities Q and W . Since the internal energy U is characterized entirely by the quantities (or parameters) that uniquely determine the state of the system at equilibrium , it is said to be a state function such that any change in energy is determined entirely by the initial ( i ) and final ( f ) states of the system: Δ U = U f − U i . However, Q and W are not state functions. Just as in the example of a bursting balloon, the gas inside may do no work at all in reaching its final expanded state, or it could do maximum work by expanding inside a cylinder with a movable piston to reach the same final state. All that is required is that the change in energy (Δ U ) remain the same. By analogy , the same change in one’s bank account could be achieved by many different combinations of deposits and withdrawals. Thus, Q and W are not state functions, because their values depend on the particular process (or path) connecting the same initial and final states. Just as it is more meaningful to speak of the balance in one’s bank account than its deposit or withdrawal content, it is only meaningful to speak of the internal energy of a system and not its heat or work content.

From a formal mathematical point of view, the incremental change d U in the internal energy is an exact differential, while the corresponding incremental changes d ′ Q and d ′ W in heat and work are not, because the definite integrals of these quantities are path dependent. These concepts can be used to great advantage in a precise mathematical formulation of thermodynamics.

Engineering Thermodynamics/First Law

• 2.1 Flow Energy
• 2.2 Examples of Work
• 2.3 Work in a Polytropic Process
• 3.1 Specific Heat
• 3.2 Latent Heat
• 3.3 Adiabatic Process
• 4.1 Joule Experiments
• 5.1 Internal Energy
• 5.2 Internal Energy for an Ideal Gas
• 6.1 Throttling

Energy as described on Wikipedia is "the property that must be transferred to an object in order to perform work on, or to heat, the object". Energy is a conserved quantity, the Law of Conservation of Energy on Wikipedia states that "energy can be converted in form, but not created or destroyed".

Common forms of energy in physics are potential and kinetic energy. The potential energy is usually the energy due to matter having certain position (configuration) in a field, commonly the gravitational field of Earth. Kinetic energy is the energy due to motion relative to a frame of reference. In thermodynamics, we deal with mainly work and heat, which are different manifestations of the energy in the universe.

Work is said to be done by a system if the effect on the surroundings can be reduced solely to that of lifting a weight. Work is only ever done at the boundary of a system. Again, we use the intuitive definition of work, and this will be complete only with the statement of the second law of thermodynamics.

Consider a piston-cylinder arrangement as found in automobile engines. When the gas in the cylinder expands, pushing the piston outwards, it does work on the surroundings. In this case work done is mechanical. But how about other forms of energy like heat? The answer is that heat cannot be completely converted into work, with no other change, due to the second law of thermodynamics.

In the case of the piston-cylinder system, the work done during a cycle is given by W , where W = −∫ F dx = −∫ p dV , where F = p A , and p is the pressure on the inside of the piston (note the minus sign in this relationship). In other words, the work done is the area under the p-V diagram. Here, F is the external opposing force, which is equal and opposite to that exerted by the system. A corollary of the above statement is that a system undergoing free expansion does no work. The above definition of work will only hold for the quasi-static case, when the work done is reversible work.

A consequence of the above statement is that work done is not a state function, since it depends on the path (which curve you consider for integration from state 1 to 2). For a system in a cycle which has states 1 and 2, the work done depends on the path taken during the cycle. If, in the cycle, the movement from 1 to 2 is along A and the return is along C , then the work done is the lightly shaded area. However, if the system returns to 1 via the path B , then the work done is larger, and is equal to the sum of the two areas.

The above image shows a typical indicator diagram as output by an automobile engine. The shaded region is proportional to the work done by the engine, and the volume V in the x -axis is obtained from the piston displacement, while the y -axis is from the pressure inside the cylinder. The work done in a cycle is given by W , where

Work done by the system is negative, and work done on the system is positive, by the convention used in this book.

Flow Energy

So far we have looked at the work done to compress fluid in a system. Suppose we have to introduce some amount of fluid into the system at a pressure p . Remember from the definition of the system that matter can enter or leave an open system. Consider a small amount of fluid of mass dm with volume dV entering the system. Suppose the area of cross section at the entrance is A . Then the distance the force pA has to push is dx = dV/A . Thus, the work done to introduce a small amount of fluid is given by pdV , and the work done per unit mass is pv , where v = dV/dm is the specific volume. This value of pv is called the flow energy .

Examples of Work

The amount of work done in a process depends on the irreversibilities present. A complete discussion of the irreversibilities is only possible after the discussion of the second law. The equations given above will give the values of work for quasi-static processes, and many real world processes can be approximated by this process. However, note that work is only done if there is an opposing force in the boundary, and that a volume change is not strictly required.

Work in a Polytropic Process

Consider a polytropic process pV n =C , where C is a constant. If the system changes its states from 1 to 2, the work done is given by

And additionally, if n=1

Before thermodynamics was an established science, the popular theory was that heat was a fluid, called caloric , that was stored in a body. Thus, it was thought that a hot body transferred heat to a cold body by transferring some of this fluid to it. However, this was soon disproved by showing that heat was generated when drilling bores of guns, where both the drill and the barrel were initially cold.

Heat is the energy exchanged due to a temperature difference. As with work, heat is defined at the boundary of a system and is a path function. Heat rejected by the system is negative, while the heat absorbed by the system is positive.

Specific Heat

The specific heat of a substance is the amount of heat required for a unit rise in the temperature in a unit mass of the material. If this quantity is to be of any use, the amount of heat transferred should be a linear function of temperature. This is certainly true for ideal gases. This is also true for many metals and also for real gases under certain conditions. In general, we can only talk about the average specific heat, c av = Q/mΔT . Since it was customary to give the specific heat as a property in describing a material, methods of analysis came to rely on it for routine calculations. However, since it is only constant for some materials, older calculations became very convoluted for newer materials. For instance, for finding the amount of heat transferred, it would have been simple to give a chart of Q(ΔT) for that material. However, following convention, the tables of c av (ΔT) were given, so that a double iterative solution over c av and T was required.

Calculating specific heat requires us to specify what we do with Volume and Pressure when we change temperature. When Volume is fixed, it is called specific heat at constant volume (C v ). When Pressure is fixed, it is called specific heat at constant pressure (C p ).

Latent Heat

It can be seen that the specific heat as defined above will be infinitely large for a phase change, where heat is transferred without any change in temperature. Thus, it is much more useful to define a quantity called latent heat , which is the amount of energy required to change the phase of a unit mass of a substance at the phase change temperature.

Adiabatic Process

An adiabatic process is defined as one in which there is no heat transfer with the surroundings, that is, the change in amount of energy dQ=0 . A gas contained in an insulated vessel undergoes an adiabatic process. Adiabatic processes also take place even if the vessel is not insulated if the process is fast enough that there is not enough time for heat to escape ( e.g. the transmission of sound through air). Adiabatic processes are also ideal approximations for many real processes, like expansion of a vapor in a turbine, where the heat loss is much smaller than the work done.

First Law of Thermodynamics

Joule experiments.

It is well known that heat and work both change the energy of a system. Joule conducted a series of experiments which showed the relationship between heat and work in a thermodynamic cycle for a system. He used a paddle to stir an insulated vessel filled with fluid. The amount of work done on the paddle was noted (the work was done by lowering a weight, so that work done = mgz ). Later, this vessel was placed in a bath and cooled. The energy involved in increasing the temperature of the bath was shown to be equal to that supplied by the lowered weight. Joule also performed experiments where electrical work was converted to heat using a coil and obtained the same result.

Statement of the First Law for a Closed System

The first law states that when heat and work interactions take place between a closed system and the environment, the algebraic sum of the heat and work interactions for a cycle is zero .

Mathematically, this is equivalent to

Q is the heat transferred, and W is the work done on or by the system. Since these are the only ways energy can be transferred, this implies that the total energy of the system in the cycle is a constant.

One consequence of the statement is that the total energy of the system is a property of the system. This leads us to the concept of internal energy.

Internal Energy

In thermodynamics, the internal energy is the energy of a system due to its temperature. The statement of first law refers to thermodynamic cycles. Using the concept of internal energy it is possible to state the first law for a non-cyclic process. Since the first law is another way of stating the conservation of energy, the energy of the system is the sum of the heat and work input, i.e. , ΔE = Q + W . Here E represents the internal energy (U) of the system along with the kinetic energy (KE) and the potential energy (PE) and is called the total energy of the system. This is the statement of the first law for non-cyclic processes, as long as they are still closed to the flow of mass ( E = U + KE + PE ). The KE and PE terms are relative to an external reference point i.e. the system is the gas within a ball, the ball travels in a trajectory that varies in height H and velocity V and subsequently KE and PE with time, but this has no affect upon the energy of the gas molecules within the ball, which is dictated only by the internal energy of the system (U). Thermodynamics does not define the nature of the internal energy, but it can be rationalised using other theories (i.e. the gas kinetic theory), but in this case is due to the KE and PE of the gas molecules within the ball, not to be mistaken with the KE and PE of the ball itself.

For gases, the value of KE and PE is quite small, so the important term is the internal energy function U . In particular, since for an ideal gas the state can be specified using two variables, the state variable u is given by u(v, T) , where v is the specific volume and T is the temperature.

Introducing this temperature dependence explicitly is important in many calculations. For this purpose, the constant-volume heat capacity is defined as follows: c v = (∂u/∂t) v , where c v is the specific heat at constant volume. A constant-pressure heat capacity will be defined later, and it is important to keep them straight. The important point here is that the other variable that U depends on "naturally" is v, so to isolate the temperature dependence of U you want to take the derivative at constant v.

Internal Energy for an Ideal Gas

In the previous section, the internal energy of an ideal gas was shown to be a function of both the volume and temperature. Joule performed an experiment where a gas at high pressure inside a bath at the same temperature was allowed to expand into a larger volume.

In the above image, two vessels, labeled A and B, are immersed in an insulated tank containing water. A thermometer is used to measure the temperature of the water in the tank. The two vessels A and B are connected by a tube, the flow through which is controlled by a stop. Initially, A contains gas at high pressure, while B is nearly empty. The stop is removed so that the vessels are connected and the final temperature of the bath is noted.

The temperature of the bath was unchanged at the end of the process, showing that the internal energy of an ideal gas was the function of temperature alone. Thus Joule's law is stated as (∂u/∂v) t = 0 .

According to the first law, dQ + dW = dE

If all the work is pressure volume work, then we have

dW = − p dV

⇒ dQ = dU + pdV = d(U + pV) - Vdp

⇒ d(U + pV) = dQ + Vdp

We define H ≡ U + pV as the enthalpy of the system, and h = u + pv is the specific enthalpy. In particular, for a constant pressure process,

ΔQ = ΔH

With arguments similar to that for c v , c p = (∂h/∂t) p . Since h , p , and t are state variables, c p is a state variable. As a corollary, for ideal gases, c p = c v + R , and for incompressible fluids, c p = c v

Throttling is the process in which a fluid passing through a restriction loses pressure. It usually occurs when fluid passes through small orifices like porous plugs. The original throttling experiments were conducted by Joule and Thompson. As seen in the previous section, in adiabatic throttling the enthalpy is constant. What is significant is that for ideal gases, the enthalpy depends only on temperature, so that there is no temperature change, as there is no work done or heat supplied. However, for real gases, below a certain temperature, called the inversion point , the temperature drops with a drop in pressure, so that throttling causes cooling, i.e. , p 1 < p 2 ⇒ T 1 < T 2 . The amount of cooling produced is quantified by the Joule-Thomson coefficient μ JT = (∂T/∂p) h . For instance, the inversion temperature for air is about 400 °C.

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3.4: The First and Second Laws of Thermodynamics

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In the chapters to follow we will frequently explain chemical and physical changes by invoking the associated changes in potential energy and we will refine the idea, making it more specific and useful to make predictions concerning the direction of spontaneous changes. Presently, however, we want to put the ideas we have already covered in a larger context. In so doing, we convey one of the bedrock principles in all of science: the First Law of Thermodynamics . While this law can be stated in a variety of ways, the most accessible and useful for our purposes is as follows: energy is conserved; it can be transformed from one form to another, but it is neither created nor destroyed by physical and chemical processes. Often referred to as the Conservation of Energy , this concept can provide a helpful logical framework when analyzing systems undergoing change. In this chapter we have shown several examples of energy conversion, but we have not emphasized the conservative nature of those changes. We do so below, using the example of a  pendulum to describe the reversible change of potential to kinetic energy. 

Figure 3-12 . A simple pendulum with its arm directed at an outward angle; if held still in this position, the bob would possess potential but not kinetic energy. Releasing the bob would allow it to fall, causing it to lose potential energy but gain kinetic energy.

In your mind’s eye, picture a pendulum that is held motionless such that its arm is not pointing straight down (Figure 3-12). You will recognize that in this state the bob of the pendulum has potential but not kinetic energy. As soon as you release the bob it begins to move, increasing in speed as it moves to the lowest point along its trajectory. As it does so, its potential energy is gradually converted to kinetic energy and, at its lowest point, all of the potential energy that was available to drive its motion is exhausted and the kinetic energy is at a maximum; the bob is moving at its greatest speed. The maximum speed it can attain is limited by the potential energy it had initially; the closer it was to the bottom of its trajectory, the lower will be its maximum speed when it gets there. After it passes the nadir of its path, its speed decreases as kinetic energy is reconverted back to potential energy. When the kinetic energy is eventually exhausted and the potential energy is maximized, the bob stops moving momentarily as it reverses direction, then begins to fall back down along its path, beginning the cycle again. 

The above illustrates the conversion of energy, from potential to kinetic and then back to potential again. Because, in accord with the First Law, energy cannot be destroyed, we would expect that the potential energy attained at the end of this sequence would be exactly the same as it was at the beginning, which is to say, that its height after one cycle will be exactly the same as it was initially. This is clearly an oversimplification and experience tells you that the amplitude of the bob’s trajectory, that is the height it attains in each cycle, will gradually decrease and the bob will eventually come to rest at its equilibrium position with the arm oriented straight down. At that point it would certainly appear that energy was lost because, when the bob rests in that position, it has neither kinetic nor potential energy. This leads us directly to the Second Law of Thermodynamics, one version of which states that no transformation of energy is ever 100% efficient , that is, some energy is always “lost” to heat. In this case friction, arising from the pendulum’s pivot point as well as to air resistance, causes a small amount of energy to be “lost” during each potential-to-kinetic and kinetic-to-potential conversion. Of course, the First Law tells us that the energy is not destroyed, thus energy “lost” is not the same as energy destroyed. It can be accounted for in the form of the heat that is generated by the friction, but that heat is not available to drive the pendulum’s motion so it eventually comes to a standstill.

Despite its seemingly prosaic form, the implications of the Second Law are truly profound. It gives us a guide to the directionality of change in the universe. For example, if you hold a book in your outstretched arms and drop it, the potential energy of the book is initially converted to kinetic energy and, upon landing, it is dissipated as heat. Nothing in the First Law would prevent that sequence of events from “running backwards”, that is, having the heat and sound caused by the book’s landing to somehow become focused and thereby induce the floor to push the book back up into your hands. Energy would not be created by that event, so it would not violate the First Law. It is the Second Law that states that only the forward scenario is possible because once potential energy is dissipated as heat it is no longer available to do useful work. The Second Law also makes it impossible to create machines that are 100% efficient, that is, a device that accomplishes an amount of work equal to the energy expended. Despite many attempts to design and build such perpetual motion machines, all have been shown to be either hoaxes or unworkable.

We will explore more aspects of the Second Law as they relate to various topics throughout this book. For example, it is helpful when explaining why mixtures of oil and water separate, how diffusion across a membrane can accomplish useful work in a cell, and why water evaporates at temperatures far below its boiling point. For the time being, however, keep the following tongue-in-cheek versions of the First and Second Laws in mind: with respect to any energy conversion, the First Law states that you can’t win, you can only break even, meaning you can’t get more energy or work out of a system than you put in; the Second Law states that you can’t even do that.

Thermodynamics In A Nutshell:

The First Law of Thermodynamics: energy is neither created nor destroyed.

The Second Law of Thermodynamics: in the conversion of one type of energy to another, some energy is always dissipated as waste heat.

It is truly difficult to overstate the importance and usefulness of these two principles. We are loathe to appeal to authority in matters of science, but it is nevertheless helpful to consider one accomplished scientist's thoughts on the centrality of these ideas to physical science. To wit, a quote from Albert Einstein: 

A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that within the framework of the applicability of its basic concepts, it will never be overthrown. [12]

Notes and References.

[12]  Albert Einstein, Autobiographical Notes (1947)

Simulation - The First Law of Thermodynamics

Specific Heat Capacity

• Turn on the heat to see how much heat is needed to change the temperature of the sample by $1K$.
• The power of the heat source is $100W = 100J/s$.
• $Q$ is given by the power input of the heat source times $t$.
• Drag the coordinate tool (the hollow square box) to make measurements on the graph.

Phase Transition of Water

• Turn on the heat to observe phase transition. You can zoom in and out of the graph with the buttons.
• The power of the heat source is $50kW = 50kJ/s$.
• Observe that the liquid-gas phase transition take a lot longer than the solid-liquid transition. Can you explain why?
• Specific heat capacity of ice, water, steam: $2.1kJ/kg^{-1}K^{-1}$, $4.186kJ/kg^{-1}K^{-1}$, $2kJ/kg^{-1}K^{-1}$.
• Latent heat of fusion and vaporization: $334kJ/kg$, $2254kJ/kg$
• The above values are approximations only. True values are temperature dependent, and also depend the heating process (e.g. isobaric vs isochoric).

Ideal Gas at Constant Temperature

Drag the piston to change the volume isothermally. The heat bath exchanges heat with the gas to keep it at constant temperature.

Adiabatic Change

Click on the "adiabatic" button to add thermal insulation to prevent heat exchange. Observe how the tempertaure changes with volume. A few background isothermal curves at $200K$ interval are included for reference.

• By switching back and forth between isothermal and adiabatic processes, raise the temperature to above $1500K$ by moving the piston alone. Don't touch the temperature slider.
• Similarly, try to lower the temperature to below $200K$ by moving the piston.

Ideal Gas at Constant Pressure or Volume

Ideal gas at constant pressure or volume (isobaric and isochoric processes).

• Turn on the heat or cold to change the pressure or the volume.
• Switch among P vs V, T vs V, and P vs T graphs.
• The power of the heat source is $500W = 500J/s$.

Heat Capacity at Constant Pressure or Volume

A lab manual based on this simulation is available here .

• Turn on the heat and observe the change in temperature.
• The heat capacity of a gas depends on how the heating process takes place.
• At constant pressure (isobaric), the total heat capacity for an ideal gas is $C_P = (\frac{f}{2}+1)nR$.
• At constant volume (isochoric), the total heat capacity is $C_V = \frac{f}{2}nR$.
• Heat the gas under isobaric and isochoric conditions and use the graphs to calculate the heat capacities.
• Change $n$ and $f$ and measure the effects on the heat capacities.
• Heat the gas to the same final temperature under isobaric and isochoric conditions. Measure the difference in the total heat input $Q$ for the two cases. Use the work done by the gas during the processes to quantitatively account for the difference.

Joule's Experiment and the First Law of Thermodynamics

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Application of The First Law of Thermodynamics

• Applications of the first law of thermodynamics.doc - 395 kB

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