Question

A sample of a gas contains $N_1$ molecules and the total kinetic energy at $-{123}^{\circ }$C is $E_1$ ergs. Another sample of a gas at ${27}^{\circ }$C has a total kinetic energy as $2E_1$ ergs. Assuming gases to be ideal, the number of gas molecules in the second sample will be:

• A. $N_1$
• B. $N_1/2$
• C. $2N_1$
• D. $4N_1$

Answer 1

The correct option is A $N_1$

The total kinetic energy of a gas is proportional to the temperature of the gas molecules and the number of molecules present in the sample.

KE = $\frac{3}{2}\times N\times K\times T$

where, $K$ is the Boltzman's constant, $T$ is the temperature and $N$ is the number of molecules of gas.

In the first case, $K{E}_1$ = $\frac{3}{2}\times K\times 150\times N_1$

In the second case, $K{E}_2$ = $\frac{3}{2}\times K\times 300\times N_2$

$\frac{K{E}_2}{K{E}_1}=2$

$\frac{2N_2}{N_1}=2$

$2N_2=2N_1$

$N_2=N_1$