# Calculating entropy for expansion

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1. Nov 19, 2014

### ChristineMarie

How do you calculate the entropy of an ideal gas with n = 1, Cv,m = 1.5R, Ti = 300K, P=3bar and expands against Pext = 1bar until final volume is twice initial volume at Tf = 200K?

2. Nov 19, 2014

### Vagn

What equations do you know that relate to entropy? How does this relate to the heat capacity? Also, you've left most of your units off!

3. Nov 19, 2014

### ChristineMarie

ΔS = nRln(Vf/Vi) + nCv,mln(Tf/Ti).
Only the mole unit, n = 1mol?
R is a constant = 8.3145J/mol.K = 0.083145L.bar/mol.K

4. Nov 19, 2014

### ChristineMarie

I'm just not sure how to incorporate the pressures, if I even need to. But if I don't need to use the pressures I would like to understand why.

5. Nov 19, 2014

### Staff: Mentor

To get the entropy change from the initial equilibrium state to the final equilibrium state of a system, you need to dream up a reversible path between these two states, and then evaluate the integral of dq/T for that path. In the case of an ideal gas, you also need to take into account the p-v-T relationship for the gas. The equation you wrote down takes all this into consideration, and has done all the work for you. So all you need to do is to substitute the volume ratio and temperature ratio in. The pressure is already implicitly taken into consideration by the equation.

Chet

6. Nov 20, 2014

Thank you!