In a sample of an ideal gas, the average translational kinetic energy of a single molecule is 7.5 × 10^-21 J. If the absolute temperature of the gas is tripled, what is the new average translational kinetic energy of a single molecule?
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Correct answer
C. 2.25 × 10^-20 J
Principle or equation
The average translational kinetic energy of a molecule in an ideal gas is directly proportional to the absolute temperature: KE_avg = (3/2)kT. Therefore, if the temperature is tripled, the average kinetic energy is also tripled.
Why this answer is correct
Initial KE_avg = 7.5 × 10^-21 J. New temperature = 3 × old temperature, so new KE_avg = 3 × 7.5 × 10^-21 J = 2.25 × 10^-20 J.
Example
If the average kinetic energy is 5.0 × 10^-21 J at 300 K, at 600 K it becomes 1.0 × 10^-20 J.
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