Question

A closed vesseln 10 L in volume contains a diatomic gas under a pressure of ${10}^{5}N/m^2$. What amount of heat should be imparted to the gas to increase the pressure in the vessel five times ?

Answer 1

Given : $P={10}^5$ $N/m^2$ $V=10$ L

Using ideal gas equation : $PV=RT$ $(\because n=1)$

$\therefore$ ${10}^5\times 10=0.0821\times T$ $⟹T=121.8K$

Now pressure is increased to 5 times i.e $P^{\prime }=5\times {10}^5$ $N/m^2$

As $V=constant$, $\frac{P}{T}=\frac{P^{\prime }}{T^{\prime }}$

$\therefore$ $\frac{{10}^5}{121.8}=\frac{5\times {10}^5}{T^{\prime }}$ $⟹T^{\prime }=609K$

Also $\Delta T=T^{\prime }-T=609-121.8=487.2K$

For diatomic gas, $\gamma =1.4$

Heat supplied at constant volume $Q_v=\frac{R\Delta T}{\gamma -1}$

$\therefore$ $Q_v=\frac{8.314\times 487.2}{1.4-1}=10126.5$ J