Q.A gas in a cylinder is at pressure P. If the masses of all the molecules are made one third of their original value and their speeds are doubled, find the resultant pressure.

[!TLDR] P ∝ (mass)(speed)²; new mass = m/3, new speed = 2v gives a net factor of 4/3. …

From kinetic theory, pressure is P = (1/3)(N/V) m <v^2>, so for a fixed number density N/V, P is proportional to m<v^2> -- the product of molecular mass and mean square speed. If the mass of every molecule is reduced to one third of its original value (m → m/3) and the speed is doubled (v → 2v, so v^2 → 4v^2), the new pressure is P' ∝ ( …

Use P ∝ m<v^2> (at fixed number density) and substitute the new mass (m/3) and new speed (2v, so v² beco …

Forgetting to square the speed factor -- doubling the speed multiplies v² (and hence pressure) by 4, not by 2, s …