# Entropy and the second law of thermodynamics

• denniszhao
In summary, the conversation discusses the use of a Stirling cycle to solve for the heat of isochoric processes. The cycle contains two isothermal processes and two isochoric processes, and the initial and final volumes are irrelevant. The change in entropy for the cycle is a function of the ratio of Vb/Va, and the hot and cold reservoirs experience opposite changes in entropy. The conversation also includes a hint about the net change in entropy being zero for the two isothermal steps.
denniszhao
Homework Statement
A Stirling engine operates between a hot reservoir at temperature TH=400K and a cold reservoir at temperature TC=300K. The working substance is n=0.15mol of ideal gas with gamma factor γ=1.4. Assume all heat going into the engine comes from the hot reservoir and all heat dissipated by the engine goes to the cold reservoir and compute the change of entropy for the universe each cycle.
I wanna first figure out the heat but I don't know their volume at that moment and how is gamma factor used in this problem.
Relevant Equations
Change of entropy for the universe=change of entropy for cold reservoir+that for hot reservoir=-QH/TH+QC/TC

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DEvens said:
Maybe you can get some hints in the following link?

http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/shegas.html
Thanks! It is to solve for the heat of the isochoric processes and now i still need the heat of those two isothermal processes which need the volume change.

rude man said:
What does "isochoric" mean? Where do you see such a process?
the stirling cycle contains two isothermal processes (constant temperature) and two isochoric processes (constant volume). you can check out the diagram attached above.

Let the smaller volume be V1 and the larger volume be V2. In terms of V1 and V2, what are QH and QC? What are ##\Delta S_H## and ##\Delta S_C##?

Here's a hint: The net change in entropy of the system plus surroundings is zero for the two isothermal steps.

Also, pay particular attention to this: "Assume all heat going into the engine comes from the hot reservoir and all heat dissipated by the engine goes to the cold reservoir"

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I wonder if this is doable.
I mean, the ratio of Vb/Va could be any number without changing the text of the problem, yet the change in entropy per cyccle is a function of this ratio.
denniszhao said:
the stirling cycle contains two isothermal processes (constant temperature) and two isochoric processes (constant volume). you can check out the diagram attached above.
I thought I deleted this post almost immediately I posted it; sorry, didn't look at the diagream carfully.

rude man said:
I wonder if this is doable.
I mean, the ratio of Vb/Va could be any number without changing the text of the problem, yet the change in entropy per cyccle is a function of this ratio.

I thought I deleted this post almost immediately I posted it; sorry, didn't look at the diagream carfully.
Here is my final hint: The initial and final volumes are irrelevant.

Chestermiller said:
Here is my final hint: The initial and final volumes are irrelevant.
That's because ln(VH/VL) - ln(VL/VH) = 0 right?

rude man said:
That's because ln(VH/VL) - ln(VL/VH) = 0 right?
Yes, aside from the minus sign.

Chestermiller said:
Yes, aside from the minus sign.
10-4.

Chestermiller said:
Here is my final hint: The initial and final volumes are irrelevant.
but i can't cancel that part tho

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@denniszhao,
EDIT: sorry, got my signs wrong. Here is correct:

## \Delta Q_C## > 0. The cold reservoir gains entropy.
## \Delta Q_H ## < 0. The hot reservoir loses entropy.

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denniszhao said:
but i can't cancel that part tho
You made an algebra mistake. The log terms cancel.

## 1. What is entropy?

Entropy is a measure of the disorder or randomness of a system. It is a thermodynamic property that increases with the degree of disorder in a system.

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

The second law of thermodynamics states that in any natural process, the total entropy of a closed system will either remain constant or increase. This means that the disorder or randomness of a system will always increase over time.

## 3. Can entropy decrease?

In a closed system, the second law of thermodynamics states that entropy cannot decrease. However, in an open system, where energy and matter can be exchanged with the surroundings, entropy can decrease locally but will always increase in the overall system.

## 4. What is the difference between entropy and energy?

Entropy and energy are two different thermodynamic properties. Energy is the ability to do work, while entropy is a measure of disorder in a system. While energy can be converted from one form to another, entropy will always increase or remain constant.

## 5. How is entropy related to the concept of time?

The concept of time is related to entropy through the second law of thermodynamics. As entropy increases, time moves forward, and as the disorder in a system increases, so does the amount of time it takes for that system to reach equilibrium.

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