Question

In an adiabatic process
PV^$\nu$ = constant
and, PV = nRT, gives
$\Rightarrow V^{\gamma -1}\propto \frac{1}{T}$
${\left(\frac{V_1}{V_2}\right)}^{\gamma -1}=\left(\frac{T_2}{T_1}\right)$
T₂ = T₁ ${\left(\frac{V_1}{V_2}\right)}^{\gamma -1}$
monoatomic gas : $\gamma =\frac{5}{3}$
$\Rightarrow T_2= (300 K) {\left(\frac{V}{2V}\right)}^{\frac{5}{3}-1}$
= 189 K (final temperature)
change in internal energy
$∆U=n\frac{f}{2}R ∆T$
$=2\left(\frac{3}{2}\right)\left(\frac{25}{3}\right)$(-111)
= - 2.7 kJ