Answer
$T=580K$
Work Step by Step
We know that
$v_{rms}=\sqrt\frac{3RT}{M}$
According to given condition,
$\sqrt\frac{3RT}{M_{He}}=\sqrt\frac{3RT}{M_H}$
For hydrogen,
$T=C^{\circ}+273=20+273=293K$
Therefore,
$\sqrt\frac{3RT}{M_{He}}=\sqrt\frac{3R(293)}{M_H}$
Squaring both sides,
$\frac{3RT}{M_{He}}=\frac{3R(293)}{M_H}$
$T=\frac{(293)\times M_{He}}{M_H}$
Using Table 19-1 to substitute the values of molar mass in the equation,
$T=\frac{(293)\times4}{2.02}=580K$
$T=580K$
