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quasar_4

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## Homework Statement

I'm trying to understand how one would plot this.

## Homework Equations

dS = dQ/T

dU = dQ-dW (W is work done by the system, Q is heat absorbed by system, U is energy)

For a closed cycle, dU = 0.

Carnot Cycle:

1- isothermal expansion at Th

2- adiabatic expansion to Tc (lower temp)

3- isothermal compression at Tc

4- adiabatic compression to Th

## The Attempt at a Solution

So in the perfectly idealized case, no new entropy is created during the Carnot cycle. For steps 1, 3, the change in entropy would be given by dS = (1/T) dQ, which could theoretically be integrated if you knew the amount of work being done by the system at each step. And overall for the whole system dU = 0 means dQ = dW for the entire system.

For steps 2, 4, the fact that they're adiabatic means no heat is transferred and there is thus no change in entropy in these steps.

So I can see that for steps 2, 4, the entropy remains a constant. Because dU = 0, the area under the U-S curve must be zero. But how do I deal (qualitatively) with steps 1,3 without knowing anything else about Q or W in these two steps? I know that for a closed cycle, the area enclosed should equal the work done by the system. Do I somehow use this?

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