Why Is Cv Used in This Example?

[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?

 

[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.