When the average speed of the molecules in a given sample of gas is doubled, the temperature is

Question

Quizplus · Accepted Answer

The temperature of a gas is directly proportional to the average kinetic energy of its molecules. The kinetic energy of a molecule is given by $ \frac{1}{2}mv^2 $, where $ m $ is the mass of the molecule and $ v $ is its velocity. If the average speed (velocity) of the molecules is doubled ($ v $ becomes $ 2v $), the kinetic energy becomes $ \frac{1}{2}m(2v)^2 = 2^2 \times \frac{1}{2}mv^2 $, which is 4 times the original kinetic energy. Since temperature is a measure of the average kinetic energy of the molecules in a gas, doubling the average speed of the molecules results in a temperature increase by a factor of 4.

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