For a particular ideal gas, which of the following graphs represents the variation of mean squared velocity of the gas m

Question

For a particular ideal gas, which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

Accepted Answer

Given: We need the graph showing variation of mean squared velocity with temperature for an ideal gas.

Find: Which graph matches the relation between mean squared velocity and temperature.

For an ideal gas,

\langle v^2 \rangle = \frac{3kT}{m}

where $k$ is the Boltzmann constant, $T$ is the temperature, and $m$ is the mass of a gas molecule.

This shows that $\langle v^2 \rangle$ is directly proportional to $T$ .

So the graph of mean squared velocity versus temperature must be a straight line with positive slope passing through the origin.

Therefore, the correct graph is Graph 3.

Answer