Answer
This gas cannot be cooled by throttling since $\mu$ is always a negative quantity.
Work Step by Step
The equation of state of this gas can be expressed as $$
v=\frac{R T}{P}+a \longrightarrow\left(\frac{\partial v}{\partial T}\right)_P=\frac{R}{P}
$$ Substituting into the Joule-Thomson coefficient relation, $$
\mu=-\frac{1}{c_p}\left(v-T\left(\frac{\partial v}{\partial T}\right)_P\right)=-\frac{1}{c_p}\left(v-T \frac{R}{P}\right)=-\frac{1}{c_p}(v-v+a)=-\frac{a}{c_p}<0
$$ Therefore, this gas cannot be cooled by throttling since $\mu$ is always a negative quantity.
