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For an ideal gas with constant properties undergoing a quasi-static process, which one of the following represents the change of entropy $(\Delta s$) from state $1$ to $2$?

- $\Delta s = C_p \ln \bigg( \dfrac{T_2}{T_1} \bigg) - R \ln \bigg( \dfrac{P_2}{P_1} \bigg) \\$
- $\Delta s = C_V \ln \bigg( \dfrac{T_2}{T_1} \bigg) - C_p \ln \bigg( \dfrac{V_2}{V_1} \bigg) \\$
- $\Delta s = C_p \ln \bigg( \dfrac{T_2}{T_1} \bigg) - C_V \ln \bigg( \dfrac{P_2}{P_1} \bigg) \\$
- $\Delta s = C_V \ln \bigg( \dfrac{T_2}{T_1} \bigg) + R \ln \bigg( \dfrac{V_1}{V_2} \bigg)$