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## Homework Statement

Temperature, pressure and volume measurements performed on 1 kg of a simple compressible substance in three stable equilibrium states yield the following results.

State 1 (T

_{1}=400 C , V

_{1}= 0,10 m

^{3}, P

_{1}=3 MPa)

State 2 (T

_{1}=400 C , V

_{1}= 0,08 m

^{3}, P

_{1}=3,5 MPa)

State 3 (T

_{1}=500 C , V

_{1}= 0,10 m

^{3}, P

_{1}=3,5 MPa)

Estimate the difference in entropy S

_{2}-S

_{1}

## Homework Equations

We don't know the gas. So I can't assume this is an ideal gas and I can't go to thermodynamics tables. I don't know the relevant equation.

## The Attempt at a Solution

First, I didn't get why the question identifies state 3. I think we can completely ignore state 3 because the question is entropy difference between state 2 and state 1.

This is clearly a compression process, (volume decreases, pressure increases) but temperature stays still. But when a gas is compressed, its pressure and temperature rises. So there must be heat transfer going on.

Entropy change = S

_{gen}+ Q/T

But we don't know the entropy generation so we can't go from here.

I assume I need a relation related with volume and pressure that yields entropy but in constant temperature. Is there a relation like that?