In a sample of an ideal gas, the average translational kinetic energy of a molecule is 6.21 × 10⁻²¹ J. If the number of molecules in the sample is doubled while the temperature remains constant, what is the new average translational kinetic energy per molecule?
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Correct answer
B. 6.21 × 10⁻²¹ J
Principle or equation
The average translational kinetic energy of a molecule in an ideal gas is directly proportional to the absolute temperature and is independent of the number of molecules.
Why this answer is correct
The average translational kinetic energy per molecule is given by (3/2)kT, where k is the Boltzmann constant and T is the absolute temperature. Since the temperature remains constant, the average kinetic energy per molecule does not change when the number of molecules is altered. Therefore, the new average kinetic energy is still 6.21 × 10⁻²¹ J.
Example
If a gas at 300 K has an average molecular kinetic energy of 6.21 × 10⁻²¹ J, doubling the number of molecules at the same temperature leaves the per-molecule average unchanged.
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