Question

Oxygen and hydrogen gas are at the same temperature T.What is the ratio of kinetic energies of oxygen molecule and hydrogen molecule if oxygen is 16 times heavier than hydrogen.

Answer 1

Answer

the ratio of kinetic energies of oxygen molecule and hydrogen molecule if oxygen is 16 times heavier than hydrogen is 1

Explanation

The average kinetic energy of a gas molecule at temperature T is given by following formula

$E =\frac{3kT}{2}$...............(1)

Here k is Boltzmann's constant ($k=1.38\times 10^{-23} JK^{-1}$).

From above equation it is clear that average kinetic energy of a gas molecule only depends on temperature.

Therefore kinetic energy of oxygen molecule $E_{1}=\frac{3kT}{2}$....2

and kinetic energy of hydrogen molecule $E_{2}=\frac{3kT}{2}$....3

the ratio of kinetic energies of oxygen molecule and hydrogen molecule if oxygen is 16 times heavier than hydrogen is given as

$\frac{E_{1}}{E_{2}} =\frac{\frac{3kT}{2}}{\frac{3kT}{2}}$

$\frac{E_{1}}{E_{2}}=1$

Therefore, the ratio of kinetic energies of oxygen molecule and hydrogen molecule if oxygen is 16 times heavier than hydrogen is 1