# Entropy change for reversible and cyclic process

• spaghetti3451
In summary, during a reversible process, the combined entropy of the gas and surroundings remains constant. Therefore, the correct answer is (C). Other answers are incorrect because during the adiabatic expansion, the entropy of the gas and surroundings remains constant, during the constant volume process the entropy of the gas increases and the entropy of the surroundings decreases, and during the isothermal compression, the entropy of the gas decreases and the entropy of the surroundings increases. However, if the process is not reversible for the surroundings, then these statements may not hold true.
spaghetti3451

## Homework Statement

An ideal diatomic gas is initially at temperature ##T## and volume ##V##. The gas is taken through three reversible processes in the following cycle: adiabatic expansion to the volume ##2V##, constant volume process to the temperature ##T##, isothermal compression to the original volume ##V##.

Which of the following statements about entropy changes in this cycle is true?

(A) The entropy of the gas remains constant during each of the three processes.
(B) The entropy of the surroundings remains constant during each of the three processes.
(C) The combined entropy of the gas and surroundings remains constant during each of the three processes.
(D) For the complete cycle, the combined entropy of the gas and surroundings increases.
(E) For the complete cycle, the entropy of the gas increases.

## The Attempt at a Solution

During a reversible process, the combined entropy of the gas and surroundings remains constant. Therefore, the correct answer is (C).

Here's why the other answers are incorrect:

During the adiabatic expansion, the heat intake is zero, so the entropy of the gas is constant. Therefore, the entropy of the surroundings is also constant.

During the constant volume process, the work done on the gas is zero (as the volume is constant) and the internal energy of the gas increases (as the temperature increases - adiabats are steeper than isotherms, so the adiabatic expansion decreased the temperature initially). So, the heat intake is positive, so the entropy of the gas increases. Therefore, the entropy of the surroundings decreases.

During the isothermal compression, the work done on the gas is positive (as the volume decreases) and the internal energy of the gas is constant (as the temperature is constant). So, the heat intake is negative, so the entropy of the system decreases. Therefore, the entropy of the surroundings increases.

Lastly, the entropy of the gas is a state variable, so the entropy of the gas is constant for the complete cycle. Therefore, the increase in entropy of the gas in the constant volume process is equal to the decrease in entropy of the gas during the isothermal compression.Do you think my analysis is correct? What mistakes have I made?

Your analysis is correct if the process is reversible with respect to both the system and the surroundings. However, the problem statement is a little ambiguous. Just because the changes are carried out reversibly for the system does not necessarily guarantee that the changes are also carried out reversibly for the surroundings. For example, if the volume increase is carried out by your hand pressing on the piston and easing off on the piston gradually as the volume increases, this is not a reversible process on your body (which represents the surroundings). On the other hand, if the volume increase is carried out by removing tiny weights from the piston as it rises to different elevations (with the weights stored at these elevations), then the process is reversible for the surroundings.

Chet

Well, this question actually came up in the 1986 Physics GRE test. I wanted to be sure of my understanding of entropy, so I posted the question.

I think what mentioned in your post is an insightful comment given that you are an experienced veteran, but it is perhaps a little too advanced for the typical undergraduate. Hopefully, for the purposes of the Physics GRE test, I won't have to understand your insight.

failexam said:
Well, this question actually came up in the 1986 Physics GRE test. I wanted to be sure of my understanding of entropy, so I posted the question.

I think what mentioned in your post is an insightful comment given that you are an experienced veteran, but it is perhaps a little too advanced for the typical undergraduate. Hopefully, for the purposes of the Physics GRE test, I won't have to understand your insight.
Well then, as I said, on that basis, your analysis is correct.

Chet

## 1. What is entropy change for reversible and cyclic process?

The entropy change for reversible and cyclic process is a measure of the change in disorder or randomness in a closed system. It is a thermodynamic property that is related to the amount of energy that is unavailable for doing work.

## 2. How is entropy change calculated?

The entropy change for reversible and cyclic process can be calculated using the formula ΔS = Q/T, where ΔS is the change in entropy, Q is the heat added or removed from the system, and T is the temperature in Kelvin.

## 3. What is the difference between reversible and irreversible processes in terms of entropy change?

In reversible processes, the entropy change is zero because the system is able to return to its initial state without any net change in entropy. In irreversible processes, the entropy change is always positive because some energy is lost as heat and cannot be recovered.

## 4. How does entropy change affect the efficiency of a cyclic process?

The entropy change for a reversible and cyclic process affects the efficiency of the process. The higher the entropy change, the lower the efficiency of the process, as more energy is lost as heat. This is why it is important to minimize entropy change in order to increase efficiency.

## 5. Can entropy change be negative?

No, entropy change cannot be negative. The second law of thermodynamics states that the entropy of a closed system always increases or remains constant. Therefore, entropy change for reversible and cyclic processes will always be zero or positive.

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