Answer
The isentropic efficiency and the second-law efficiency of an isentropic compressor are both $100 \%$.
Work Step by Step
In an isentropic compressor, $s_2 = s_1$ and $h_{2s} = h_2$. Applying these to the two the efficiency definitions, we obtain $$
\begin{aligned}
& \eta_{\mathrm{s}, \text { Comp }}=\frac{w_{\text {isen }}}{w}=\frac{h_{2 s}-h_1}{h_2-h_1}=\frac{h_2-h_1}{h_2-h_1}=1=100 \% \\
& \eta_{\text {II, Comp }}=\frac{w_{\mathrm{rev}}}{w}=\frac{h_2-h_1-T_0\left(s_2-s_1\right)}{h_2-h_1}=\frac{h_2-h_1}{h_2-h_1}=1=100 \%
\end{aligned}
$$ Thus, the isentropic efficiency and the second-law efficiency of an isentropic compressor are both $100 \%$.
