# Homework Help: Entropy change explanation

1. Mar 9, 2010

### noob314

Can someone explain to me why Cv is used in this example?

Determine delta S for the conversion of a monatomic ideal gas from state 1 to state 2.
Cv = (3/2)R, Cp = (5/2)R
State 1: V1 = 22.0L, P1 = 1.25atm, T1 = 308K, n=0.917mol
State 2: V2 = 34.0L, P2 = 0.700atm, T2=325K, n=0.917mol

delta S = nR(V2/V1) + nCvln(T2/T1)

From what I can see, the process doesn't look like it's carried out in either constant pressure nor constant volume. If that answer is correct, then why is Cp not used?

2. Mar 10, 2010

### Mapes

The entropy change comes from the differential energy equation

$$dU=T\,dS-P\,dV\Rightarrow dS=\frac{dU}{T}+\frac{P\,dV}{T}$$

the ideal gas equation

$$PV=nRT$$

and the equation for ideal gas energy

$$U=U_0+nc_VT\Rightarrow dU=nc_V\,dT=n(c_P-R)dT$$

$c_V=c_P-R$ is just a constant here. It doesn't imply that any process occurs at constant volume or pressure.