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When the temperature of a gas increases, the average speed of its

June 1, 2025 by rawan239

When the temperature of a gas increases, the average speed of its molecules

remains the same

decreases

increases

either increases or decreases depending on the gas

This question was previously asked in

UPSC Geoscientist – 2023

Download PDF Attempt Online

The correct answer is C) increases.

According to the kinetic theory of gases, the absolute temperature of an ideal gas is directly proportional to the average kinetic energy of its molecules. Kinetic energy is given by the formula $KE = \frac{1}{2}mv^2$, where $m$ is the mass of a molecule and $v$ is its speed. As temperature increases, the average kinetic energy of the molecules increases. Since the mass of the molecules remains constant, an increase in average kinetic energy implies an increase in the average value of $v^2$. The average speed of the molecules is related to the average of the square of the speed (root-mean-square speed), and both increase with increasing temperature.

The root-mean-square speed ($v_{rms}$) of gas molecules is given by the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant, $T$ is the absolute temperature, and $m$ is the mass of a molecule. This formula clearly shows that the average speed of gas molecules increases with the square root of the absolute temperature. Therefore, as the temperature of a gas increases, the average speed of its molecules also increases.

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