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What happens to the pressure of a gas when its mass is halved and speed is doubled?

1. P' = 1/3 × (m/V) × v_rms^2
2. P' = 2P
3. P' = 1/2 × (m/V) × v_rms^2
4. P' = P

Correct answer: P' = 2P

Solution

Pressure is proportional to the product of mass density and the square of the root mean square (rms) speed. Halving the mass reduces density by half, but doubling the speed increases the square of the speed by four times. The net effect is a doubling of pressure.

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