Question:
The average kinetic energy of a gas molecule is
The average kinetic energy of a gas molecule is
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Notice that the average kinetic energy depends \textbf{only} on temperature. It does not matter if the gas is oxygen, hydrogen, or helium—at the same temperature, every molecule has the same average kinetic energy!
Updated On: Apr 24, 2026
- $\frac{1}{2}kT$
- $\frac{3}{2}kT$
- $kT$
- $\frac{2}{3}kT$
- $\frac{5}{2}kT$
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The Correct Option is B
Solution and Explanation
Concept:
Physics - Kinetic Theory of Gases (Law of Equipartition of Energy).
Step 1: Understand the degree of freedom.
For a monoatomic gas molecule (which serves as the standard "gas molecule" unless specified otherwise), there are 3 degrees of freedom (translational motion in $x, y, z$ directions).
Step 2: Apply the Law of Equipartition of Energy.
This law states that the average kinetic energy associated with each degree of freedom of a molecule is $\frac{1}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the absolute temperature.
Step 3: Calculate total average kinetic energy.
Since there are 3 degrees of freedom: $$ KE_{avg} = 3 \times \left( \frac{1}{2}kT \right) = \frac{3}{2}kT $$
Step 4: Conclusion.
The average kinetic energy per molecule is $\frac{3}{2}kT$.
Physics - Kinetic Theory of Gases (Law of Equipartition of Energy).
Step 1: Understand the degree of freedom.
For a monoatomic gas molecule (which serves as the standard "gas molecule" unless specified otherwise), there are 3 degrees of freedom (translational motion in $x, y, z$ directions).
Step 2: Apply the Law of Equipartition of Energy.
This law states that the average kinetic energy associated with each degree of freedom of a molecule is $\frac{1}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the absolute temperature.
Step 3: Calculate total average kinetic energy.
Since there are 3 degrees of freedom: $$ KE_{avg} = 3 \times \left( \frac{1}{2}kT \right) = \frac{3}{2}kT $$
Step 4: Conclusion.
The average kinetic energy per molecule is $\frac{3}{2}kT$.
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