$9\mathrm{.}5$ The equation of state for helium gas may be written in the form

$p{V}_m=RT(1+\frac{B}{V_m})$ where $B$ is a function of temperature only and

has the following values:

$\frac{T}{K},10,20,30,40,50,60,70$

$\frac{B}{{10}^{-6}}{m}^{3}mo{l}^{-1},-23\mathrm{.}3,-4\mathrm{.}0,+2\mathrm{.}4,+5\mathrm{.}6,+7\mathrm{.}6,+8\mathrm{.}9,+9\mathrm{.}8$

Determine $(a)$ the Boyle temperature, $(b)$ the inversion temperature,

$($c$)$ the temperature drop when helium initially at $20K$ and $10$atm

pressure expands into a very large empty vessel under conditions of

thermal isolation.

$[$For helium, $C_{mV}=\frac{3}{2}R.]$