Answer
a) $COP= 3.093$
b) $COP= 3.582$
Work Step by Step
(a) The expansion process through the expansion valve is isenthalpic: $h_4=h_3$.
$$
\begin{aligned}
& q_L=h_1-h_4=402.49-243.19=159.3\ \mathbf{k J} / \mathbf{k g} \\
& q_H=h_2-h_3=454.00-243.19=210.8 \mathrm{~kJ} / \mathrm{kg} \\
& w_{\text {in }}=h_2-h_1=454.00-402.49=51.51\ \mathbf{k J} / \mathbf{k g} \\
& \mathrm{COP}=\frac{q_L}{w_{\text {in }}}=\frac{159.3 \mathrm{~kJ} / \mathrm{kg}}{51.51 \mathrm{~kJ} / \mathrm{kg}}=3.093
\end{aligned}
$$ (b) Ideal vapor-compression refrigeration cycle solution: $$
\begin{aligned}
& q_L=h_1-h_4=399.04-249.80=149.2 \mathrm{~kJ} / \mathbf{k g} \\
& q_H=h_2-h_3=440.71-249.80=190.9 \mathrm{~kJ} / \mathrm{kg} \\
& w_{\text {in }}=h_2-h_1=440.71-399.04=41.67 \mathrm{~kJ} / \mathbf{k g} \\
& \mathrm{COP}=\frac{q_L}{w_{\text {in }}}=\frac{149.2 \mathrm{~kJ} / \mathrm{kg}}{41.67 \mathrm{~kJ} / \mathrm{kg}}=3.582
\end{aligned}
$$
