GRE Entropy Question: Problem 21 in Attached File - Solution Debate

In summary, the problem asks for the calculation of entropy in a reversible process, where entropy is conserved. The correct answer is C, and there is an exchange of energy between the system and surroundings. This is true for both adiabatic and reversible processes, where the change in entropy of the system is equal to the change in entropy of the surroundings. The calculation can be done using the definition of reversible process and through energy conservation.
  • #1
Silviu
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11

Homework Statement


It is problem 21 in the attached file.

Homework Equations

The Attempt at a Solution


The answer seems to be C. I thought it is D. Can someone explain it to me please?
 

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  • #2
Key word in the problem statement is 'reversible'. For reversible processes entropy is conserved.
 
  • #3
BvU said:
Key word in the problem statement is 'reversible'. For reversible processes entropy is conserved.
So for a reversible process, the entropy is conserved for both the system and the surroundings (but not for each of them individually)?
 
  • #4
Correct: there is an exchange of energy between the two.
 
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  • #5
BvU said:
Correct: there is an exchange of energy between the two.
Thank you so much!
 
  • #6
Is it really clear to you that (A) and (B) are not true ?
 
  • #7
BvU said:
Is it really clear to you that (A) and (B) are not true ?
For the gas it is clear that the entropy is constant only during the adiabatic transformation. However I am not sure how can I calculate the entropy of the surroundings
 
  • #8
Nothing happens to the surroundings (if all that occurs is this adiabatic expansion). There is no ##\delta Q##, so no ## \delta S##.
 
  • #9
BvU said:
Nothing happens to the surroundings (if all that occurs is this adiabatic expansion). There is no ##\delta Q##, so no ## \delta S##.
No, sorry. I meant in the other 2 cases the isothermal and constant volume. How can I know that the change in entropy of the system exactly compensate the one of the surrounding? It is just by the definition of reversible process or there is something more to it?
 
  • #10
Not much more to it. Reversibility means you can also go through the process in the other direction - in which case ##\delta S## comes out the same value but with opposite sign. That can only be correct if it is zero.
Silviu said:
change in entropy of the system exactly compensate the one of the surrounding
More through energy conservation plus ##dQ = TdS##.
 
  • #11
Silviu said:
No, sorry. I meant in the other 2 cases the isothermal and constant volume. How can I know that the change in entropy of the system exactly compensate the one of the surrounding? It is just by the definition of reversible process or there is something more to it?
For a reversible process, when heat is transferred, the temperature difference between the gas and its surroundings is infinitesimal. There has to be some difference in temperature, otherwise heat won't flow, but since the two are essentially at the same temperature, the decrease in entropy of one is equal to the increase of the other.
 
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1. What is entropy in the context of the GRE question?

Entropy is a measure of disorder or randomness in a system. In the context of the GRE question, it refers to the amount of disorder in a given chemical reaction or physical process.

2. How is entropy related to the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of a closed system (one that does not exchange matter or energy with its surroundings) will always increase over time. This means that as a system becomes more disordered, its entropy increases.

3. How is entropy calculated?

The change in entropy of a system can be calculated using the equation ΔS = Q/T, where ΔS is the change in entropy, Q is the amount of heat transferred, and T is the temperature in Kelvin. Entropy is measured in units of joules per Kelvin (J/K).

4. How does entropy affect the spontaneity of a reaction?

In general, chemical reactions that result in an increase in entropy are more likely to be spontaneous, while those that result in a decrease in entropy are less likely to be spontaneous. This is because increasing entropy leads to a more disordered state, which is favored by the second law of thermodynamics.

5. How can I use entropy to predict the direction of a chemical reaction?

In addition to considering the change in enthalpy (ΔH) and temperature (ΔT), the change in entropy (ΔS) can also be used to predict the direction of a chemical reaction. If ΔS is positive, the reaction is more likely to be spontaneous in the forward direction. However, if ΔS is negative, the reaction is more likely to be spontaneous in the reverse direction.

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