Question

The translational kinetic energy of all the molecules of Helium having a volume $V$ exerting a pressure $P$ is $1000\text{J}$. The total kinetic energy (in $\text{Joule}$) of all the molecules of $N_2$ 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,
Translational kinetic energy $\left(E\right)=\frac{3}{2}PV$
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, $E^{\prime }=\frac{3}{2}\left(2P\right)V$ ... (2)
From equation (1) and (2),
$\frac{1000}{E^{\prime }}=\frac{\frac{3}{2}PV}{\frac{3}{2}\left(2P\right)V}$
$\Rightarrow E^{\prime }=2\times 1000\text{J}=2000\text{J}$