Question

The translational kinetic energy of all the molecules of $1$ mole of Helium gas having a volume $V$ exerting a pressure $P$ is $1000\text{J}$. The total kinetic energy (in $\text{Joule}$) of all the molecules of $1$ mole of $N_2$ gas having the same volume $V$ and exerting a pressure $2P$ is :

• A. $4000\text{J}$
• B. $3000\text{J}$
• C. $2000\text{J}$
• D. $1000\text{J}$

Answer 1

The correct option is C $2000\text{J}$

We know that,
Total translational kinetic energy of $1$ mole of a gas :
$\left(E\right)=\frac{3}{2}PV$
where $P=$ Pressure
$V=$ Volume
According to question,
For Helium gas,
$1000=\frac{3}{2}\times PV$ ... (1)
Now, for nitrogen
Let K.E be $E^{\prime }$ when pressure $=2P$ and volume $=V$
So, $E^{\prime }=\frac{5}{2}\left(2P\right)V$ ... (2)
$(\because N_2$ got translational as well as rotational kinetic energy$)$
From equation (1) and (2),
$\frac{1000}{E^{\prime }}=\frac{\frac{3}{2}PV}{\frac{5}{2}\left(2P\right)V}$
$\Rightarrow E^{\prime }=\frac{10}{3}\times 1000\text{J}=\frac{10000}{3}\text{J}$