Question

Mean speed of molecule of hydrogen sample equal to the mean speed of molecule of helium sample calculate the ratio of temperature

Answer 1

Answer: The ratio of temperature is 1:2.

Explanation:

Average speed of the gas  molecule :

$\bar{u}=\sqrt{\frac{8RT}{\pi M}}$

R = universal gas constant

T= temperature of the gas

M = molar mass of the gas

Mean speed of molecule of hydrogen gas:

$\bar{u_{H_2}}=\sqrt{\frac{8RT_1}{\pi 2 g/mol}}$

Mean speed of molecule of helium $\bar{u_{He}}=\sqrt{\frac{8RT_2}{\pi 4 g/mol}}$

$\bar{u_{H_2}}=\bar{u_{He}}$

$\frac{\bar{u_{H_2}}}{\bar{u_{He}}}=\sqrt{\frac{\frac{8RT_1}{\pi 2 g/mol}}{\frac{8RT_2}{\pi 4 g/mol}}}$

$\frac{T_1}{T_2}=\frac{1}{2}$

The ratio of temperature is 1:2.