Question

For a monatomic ideal gas, temperature is proportional to : the square of the average atomic velocity.

Answer 1

Answer:

the square of the average atomic velocity.

Explanation:

From the formulas for kinetic energy and temperature for a monoatomic gas, which has three translational degrees of freedom, the relationship between root mean square velocity and temperature is as follows:

$v_{rms}=\sqrt{\frac{3RT}{M}}$ (1)

Where  $v_{rms}$ is the root mean square velocity, M is the molar mass of the gas, R is the universal constant of the ideal gases and T is the temperature.

The root mean square velocity is a measure of the velocity of the particles in a gas. It is defined as the square root of the mean square velocity of the gas molecules:

$v_{rms}=\sqrt{}$ (2)

substituting 2 in 1, we find the relationship between mean square speed and temperature:

$\sqrt{}=\sqrt{\frac{3RT}{M}}\\T=\frac{M}{3R}\\\\T\sim$