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(D) The average speed of gas molecules is given by $v_{avg} = \sqrt{\frac{8RT}{\pi M}}$.Since $v_{avg} \propto \sqrt{T}$,if the average speed is doubl

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$4$

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(D) The average speed of gas molecules is given by $v_{avg} = \sqrt{\frac{8RT}{\pi M}}$.Since $v_{avg} \propto \sqrt{T}$,if the average speed is doubled,the temperature $T$ must increase by a factor of $2^2 = 4$.For an ideal gas,the pressure $P$ is related to temperature $T$ by the ideal gas law $PV = nRT$.In a closed container,the volume $V$ and the number of moles $n$ remain constant.Therefore,$P \propto T$.Since the temperature $T$ increases by a factor of $4$,the pressure $P$ will also increase by a factor of $4$.

One mole of an ideal gas at $STP$ is heated in an insulated closed container until the average speed of its molecules is doubled. Its pressure would therefore increase by what factor?

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