Clarification required on whether to use $C_v$ or $C_p$ in this question on finding entropy change
The correct form can be identified as follows. Start from the combined 1st and 2nd laws:

$$\begin{aligned} d S &amp; = \frac{dU}{T} +  \frac{p}{T}dV \end{aligned}$$

For an ideal gas 

$$\begin{aligned} d U &amp;= nC_V dT \\ \frac{p}{T} &amp;= \frac{nR}{V} \end{aligned}$$

such that

$$\begin{aligned} d S &amp; = nC_V \frac{dT}{T} +  nR \frac{dV}{V} \end{aligned}$$

Integrating

$$\begin{aligned} \Delta S &amp; = nC_V \ln \left( \frac{T_2}{T_1} \right) +  nR \ln \left( \frac{V_2}{V_1} \right) \end{aligned}$$

Substitute in the ideal gas law in the right-hand side (note $n$ is constant)

$$\begin{aligned} \Delta S &amp; = nC_V \ln \left( \frac{T_2}{T_1} \right) +  nR \ln \left( \frac{P_1 T_2}{P_2 T_1} \right) \\ &amp; = n(C_V +R) \ln \left( \frac{T_2}{T_1} \right) +  nR \ln \left( \frac{P_1 }{P_2 } \right) \\ &amp; = nC_p \ln \left( \frac{T_2}{T_1} \right) +  nR \ln \left( \frac{P_1 }{P_2 } \right) \end{aligned}$$