Thermodynamics

Step 1: Understanding the relationship between kinetic energy and temperature.
In a monoatomic ideal gas, the average kinetic energy of a molecule is related to the temperature by the equation:

Step 2: Analyzing the options.
(A) : Incorrect — This is not correct, the factor should be .
(B) : Correct — This is the correct equation for the total energy of the gas molecules in thermal equilibrium.
(C) : Incorrect — This is a repetition of option B.
(D) : Incorrect — This refers to the x-component of the velocity, which is incorrect for the total kinetic energy.

Step 3: Conclusion.
The correct answer is (B) .