Question

At what temperature will be total kinetic energy ($KE$) of 0.30 mole of $He$ be the same as the total $KE$ of 0.40 mole of $Ar$ at 400 $K$

• A. 400 $K$
• B. 373 $K$
• C. 533 $K$
• D. 300 $K$

Answer 1

The correct option is C 533 $K$

The total kinetic energy ($KE$) of 0.30 mole of $He$ at 533 $K$ will be the same as the total $KE$ of 0.40 mole of $Ar$ at 400 $K$.
Total kinetic energy is directly proportional to the absolute temperature and inversely proportional to the number of moles.

$\frac{KE}{K{E}^{\prime }}=\frac{T}{N}\times \frac{N^{\prime }}{T^{\prime }}$

Here, $KE$ and $K{E}^{\prime }$ are the total kinetic energies of $He$ and $Ar$, $T$ and $T^{\prime }$ are the absolute temperatures of $He$ and $Ar$ and $N$ and $N^{\prime }$ are the number of moles of $He$ and $Ar$ respectively.

$\frac{KE}{K{E}^{\prime }}=\frac{T}{0.30}\times \frac{0.40}{400}$

$T=533K$

So, the correct option is $C$