 # Entropy Change In Reversible And Irreversible Process Pdf

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Published: 08.06.2021  So far we have been considering the change of entropy only in reversible-processes. Let us turn now to the problem associated with the change of entropy in irreversible processes and, in particular, in irreversible processes proceeding in an isolated system, which are of the greatest interest. Isolated is the name given to a system with a rigid boundary with ideal heat insulation.

You are expected to be able to define and explain the significance of terms identified in bold. A change is said to occur reversibly when it can be carried out in a series of infinitesimal steps, each one of which can be undone by making a similarly minute change to the conditions that bring the change about. For example, the reversible expansion of a gas can be achieved by reducing the external pressure in a series of infinitesimal steps; reversing any step will restore the system and the surroundings to their previous state.

## Background

Figure 1. The ice in this drink is slowly melting. Eventually the liquid will reach thermal equilibrium, as predicted by the second law of thermodynamics.

There is yet another way of expressing the second law of thermodynamics. This version relates to a concept called entropy. By examining it, we shall see that the directions associated with the second law—heat transfer from hot to cold, for example—are related to the tendency in nature for systems to become disordered and for less energy to be available for use as work.

The entropy of a system can in fact be shown to be a measure of its disorder and of the unavailability of energy to do work. Recall that the simple definition of energy is the ability to do work. Entropy is a measure of how much energy is not available to do work. Although all forms of energy are interconvertible, and all can be used to do work, it is not always possible, even in principle, to convert the entire available energy into work.

That unavailable energy is of interest in thermodynamics, because the field of thermodynamics arose from efforts to convert heat to work. We can see how entropy is defined by recalling our discussion of the Carnot engine. We noted that for a Carnot cycle, and hence for any reversible processes,. Q c and Q h are absolute values of the heat transfer at temperatures T c and T h , respectively.

The reason is that the entropy S of a system, like internal energy U , depends only on the state of the system and not how it reached that condition. Entropy is a property of state. That will be the change in entropy for any process going from state 1 to state 2. See Figure 2.

Figure 2. Now let us take a look at the change in entropy of a Carnot engine and its heat reservoirs for one full cycle. We assume the reservoirs are sufficiently large that their temperatures are constant. This result, which has general validity, means that the total change in entropy for a system in any reversible process is zero. The entropy of various parts of the system may change, but the total change is zero. Furthermore, the system does not affect the entropy of its surroundings, since heat transfer between them does not occur.

Thus the reversible process changes neither the total entropy of the system nor the entropy of its surroundings. Sometimes this is stated as follows: Reversible processes do not affect the total entropy of the universe. Real processes are not reversible, though, and they do change total entropy. We can, however, use hypothetical reversible processes to determine the value of entropy in real, irreversible processes.

Example 1 illustrates this point. Spontaneous heat transfer from hot to cold is an irreversible process. See Figure 3. Figure 3. Remember that the total change in entropy of the hot and cold reservoirs will be the same whether a reversible or irreversible process is involved in heat transfer from hot to cold.

So we can calculate the change in entropy of the hot reservoir for a hypothetical reversible process in which J of heat transfer occurs from it; then we do the same for a hypothetical reversible process in which J of heat transfer occurs to the cold reservoir. This produces the same changes in the hot and cold reservoirs that would occur if the heat transfer were allowed to occur irreversibly between them, and so it also produces the same changes in entropy.

First, for the heat transfer from the hot reservoir,. There is an increase in entropy for the system of two heat reservoirs undergoing this irreversible heat transfer. We will see that this means there is a loss of ability to do work with this transferred energy.

Entropy has increased, and energy has become unavailable to do work. It is reasonable that entropy increases for heat transfer from hot to cold. The decrease in entropy of the hot object is therefore less than the increase in entropy of the cold object, producing an overall increase, just as in the previous example. This result is very general:. There is an increase in entropy for any system undergoing an irreversible process. With respect to entropy, there are only two possibilities: entropy is constant for a reversible process, and it increases for an irreversible process.

There is a fourth version of the second law of thermodynamics stated in terms of entropy :. The total entropy of a system either increases or remains constant in any process; it never decreases. For example, heat transfer cannot occur spontaneously from cold to hot, because entropy would decrease. Entropy is very different from energy. Entropy is not conserved but increases in all real processes. Reversible processes such as in Carnot engines are the processes in which the most heat transfer to work takes place and are also the ones that keep entropy constant.

Thus we are led to make a connection between entropy and the availability of energy to do work. What does a change in entropy mean, and why should we be interested in it? One reason is that entropy is directly related to the fact that not all heat transfer can be converted into work. Example 2 gives some indication of how an increase in entropy results in less heat transfer into work. Figure 4. The increase in entropy caused by the heat transfer to a colder reservoir results in a smaller work output of J.

There is a permanent loss of J of energy for the purpose of doing work. There is J less work from the same heat transfer in the second process. This result is important.

The same heat transfer into two perfect engines produces different work outputs, because the entropy change differs in the two cases. In the second case, entropy is greater and less work is produced. Entropy is associated with the un availability of energy to do work.

When entropy increases, a certain amount of energy becomes permanently unavailable to do work. The energy is not lost, but its character is changed, so that some of it can never be converted to doing work—that is, to an organized force acting through a distance. For instance, in Example 2, J less work was done after an increase in entropy of 9.

In the early, energetic universe, all matter and energy were easily interchangeable and identical in nature. Gravity played a vital role in the young universe. Although it may have seemed disorderly, and therefore, superficially entropic, in fact, there was enormous potential energy available to do work—all the future energy in the universe.

As the universe matured, temperature differences arose, which created more opportunity for work. Stars are hotter than planets, for example, which are warmer than icy asteroids, which are warmer still than the vacuum of the space between them. Most of these are cooling down from their usually violent births, at which time they were provided with energy of their own—nuclear energy in the case of stars, volcanic energy on Earth and other planets, and so on. Without additional energy input, however, their days are numbered.

As entropy increases, less and less energy in the universe is available to do work. As these are used, a certain fraction of the energy they contain can never be converted into doing work. Eventually, all fuels will be exhausted, all temperatures will equalize, and it will be impossible for heat engines to function, or for work to be done.

Entropy increases in a closed system, such as the universe. But in parts of the universe, for instance, in the Solar system, it is not a locally closed system. The Sun will continue to supply us with energy for about another five billion years. We will enjoy direct solar energy, as well as side effects of solar energy, such as wind power and biomass energy from photosynthetic plants. But in terms of the universe, and the very long-term, very large-scale picture, the entropy of the universe is increasing, and so the availability of energy to do work is constantly decreasing.

Eventually, when all stars have died, all forms of potential energy have been utilized, and all temperatures have equalized depending on the mass of the universe, either at a very high temperature following a universal contraction, or a very low one, just before all activity ceases there will be no possibility of doing work. Either way, the universe is destined for thermodynamic equilibrium—maximum entropy.

This is often called the heat death of the universe , and will mean the end of all activity. However, whether the universe contracts and heats up, or continues to expand and cools down, the end is not near. Calculations of black holes suggest that entropy can easily continue for at least 10 years. Entropy is related not only to the unavailability of energy to do work—it is also a measure of disorder.

This notion was initially postulated by Ludwig Boltzmann in the s. For example, melting a block of ice means taking a highly structured and orderly system of water molecules and converting it into a disorderly liquid in which molecules have no fixed positions. See Figure 5. There is a large increase in entropy in the process, as seen in the following example. Figure 5. When ice melts, it becomes more disordered and less structured.

The systematic arrangement of molecules in a crystal structure is replaced by a more random and less orderly movement of molecules without fixed locations or orientations. Its entropy increases because heat transfer occurs into it. Entropy is a measure of disorder. Find the increase in entropy of 1.

Here Q is the heat transfer necessary to melt 1. Now the change in entropy is positive, since heat transfer occurs into the ice to cause the phase change; thus,. T is the melting temperature of ice. ## Entropy of reversible and irreversible processes

Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up. What difference between the two processes in molecular level is responsible for this change? It means an infinitesimal change in something as it undergoes a process. The something of interest here is a thermodynamic state function of a system, its surroundings, or the universe.

Let a system change from state 1 to state 2 by a reversible process A and return to state 1 by another reversible process B. Then 1A2B1 is a reversible cycle. Therefore, the Clausius inequality gives:. If the system is restored to the initial state from 1 to state 2 by an irreversible process C, then 1A2C1 is an irreversible cycle. Then the Clausius inequality gives:. Subtracting the above equation from the first one,. Since the process 2B1 is reversible,.

In order to calculate the change in entropywhen a system goes from one state a , to another b , we have to find a reversible path from a to b, and then calculate the integral:. Since we are at liberty choosing the reversible path, it is convinient to choose a path that gives an easy integration. From the isothermal expansion for an ideal gas from V 1 to V 2 , we have:. At moderate pressures about 1 bar and not too low temperatures, only a small error is introduced when treating a real gas as an ideal gas. The entropy of a liquid or a solid changes very little with pressure, and usually this entropy change may be ignored. ## 13.4: Entropy Changes in Reversible Processes

Consider a system in contact with a heat reservoir during a reversible process. If there is heat absorbed by the reservoir at temperature , the change in entropy of the reservoir is. In general, reversible processes are accompanied by heat exchanges that occur at different temperatures. To analyze these, we can visualize a sequence of heat reservoirs at different temperatures so that during any infinitesimal portion of the cycle there will not be any heat transferred over a finite temperature difference.

In science, a process that is not reversible is called irreversible. This concept arises frequently in thermodynamics. In thermodynamics, a change in the thermodynamic state of a system and all of its surroundings cannot be precisely restored to its initial state by infinitesimal changes in some property of the system without expenditure of energy.

### Entropy Changes in Reversible and Irreversible Processes

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