During an adiabatic compression, $830 \mathrm{~J}$ of work is done on 2 moles of a diatomic ideal gas to…
During an adiabatic compression, $830 \mathrm{~J}$ of work is done on 2 moles of a diatomic ideal gas to reduce its volume by $50 \%$. The change in its temperature is nearly: $\left(\mathrm{R}=8.3 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)$
$40 \mathrm{~K}$
$33 \mathrm{~K}$
$20 \mathrm{~K}$
$14 \mathrm{~K}$
Solution
Given : work done, $W=830 \mathrm{~J}$
No. of moles of gas, $\mu=2$
For diatomic gas $\gamma=1.4$
Work done during an adiabatic change
$
\begin{aligned}
&W=\frac{\mu R\left(T_1-T_2\right)}{\gamma-1} \\
&\Rightarrow 830=\frac{2 \times 8.3(\Delta T)}{1.4-1}=\frac{2 \times 8.3(\Delta T)}{0.4} \\
&\Rightarrow \Delta T=\frac{830 \times 0.4}{2 \times 8.3}=20 \mathrm{~K}
\end{aligned}
$