Answer
$s_{2}-s_{1}= 0.242\text{ kj/kg}\cdot\text{K}$
Work Step by Step
The entropy change across the shock is determined to be
$$
\begin{aligned}
s_2-s_1 & =c_p \ln \frac{T_2}{T_1}-R \ln \frac{P_2}{P_1} \\
& =(1.005 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}) \ln (2.3230)-(0.287 \mathrm{~kJ} / \mathrm{kg} \cdot \mathrm{K}) \ln (8.2208) \\
& =\mathbf{0 . 2 4 2~ k J} / \mathbf{k g} \cdot \mathbf{K}
\end{aligned}
$$
