What is the average kinetic energy of a gas molecule at temperature T?

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Question: What is the average kinetic energy of a gas molecule at temperature T?

Options:

Correct Answer: (3/2)kT

Solution:

The average kinetic energy of a gas molecule is given by the formula KE_avg = (3/2)kT, where k is the Boltzmann constant.

What is the average kinetic energy of a gas molecule at temperature T?

What is the average kinetic energy of a gas molecule at temperature T?

Step 1: Understand that kinetic energy is the energy of motion. Gas molecules are always moving.
Step 2: Know that temperature (T) is a measure of how much energy the molecules have. Higher temperature means more energy.
Step 3: Learn about the Boltzmann constant (k), which is a number that helps relate temperature to energy. Its value is approximately 1.38 x 10^-23 J/K.
Step 4: Use the formula for average kinetic energy of a gas molecule: KE_avg = (3/2)kT.
Step 5: Plug in the values of k and T into the formula to calculate the average kinetic energy.

Kinetic Energy of Gas Molecules – The average kinetic energy of gas molecules is directly proportional to the temperature of the gas, as described by the equation KE_avg = (3/2)kT.
Boltzmann Constant – The Boltzmann constant (k) relates the average kinetic energy of particles in a gas to the temperature, providing a bridge between macroscopic and microscopic physics.