Question

One mole of helium in a vessel gets heat from outside and starts expanding to make its volume $2$ times the original volume. The heat capacity of the gas in this process is constant and is $\frac{R}{2}$. What is the final temperature (in $K$ ) of the gas, if the initial temperature is $200K$ and initial pressure is $40kPa$ ?
(Here, $R=$ Universal gas constant)

Answer 1

Answer: 100

The process is polytropic.
$C=C_v-\frac{R}{m-1}$
$\frac{R}{2}=\frac{3}{2}R-\frac{R}{m-1}$
$\Rightarrow m=2$
$P{V}^2=C$
$40\times V_0^2=P{\left(2V_0\right)}^2$
$P=10kPa$
$\frac{PV}{T}=\frac{P_0{V}_0}{T_0}$
$\frac{10\times 2V_0}{T}=\frac{40\times V_0}{200}$
$\Rightarrow T=100K$