Question

Two flasks $A$ and $B$ of equal volumes are maintained at a temperature of $300\text{K}$ and $700\text{K}$. They contain equal masses of $He\left(g\right)$ and $N_2\left(g\right)$ respectively. What is the ratio of the translational kinetic energy of the gas in flask $A$ to that of flask $B$ ?

• A. 1 : 3
• B. 3 : 1
• C. 3 : 49
• D. None of these

Answer 1

The correct option is B 3 : 1

Consider that the mass of $N_2$ and $He$ taken to be $w$ g.
Moles of gas= $\frac{Givenmass}{Molarmass}$
Moles of $N_2$ = $\frac{w}{28}$
Moles of $He$ = $\frac{w}{4}$
Moles ratio $=\frac{n_{He}}{n_{N_2}}=\frac{\frac{w}{4}}{\frac{w}{28}}=\frac{7}{1}$
Translational kinetic energy for $n$ mol of gas particles = $\frac{3}{2}nRT$
Ratio of translational K.E. $=\frac{n_{He}}{n_{N_2}}.\frac{T_{He}}{T_{N_2}}$
$=\frac{7}{1}\times \frac{300}{700}=3:1$