Question

Gas at a pressure P0 is contained in a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure will be equal to

(A) 2 P0

(B) 4 P0

(C) (P0/2)

(D) P0

Answer 1

The correct option (A) 2 P0

Explanation:

Vrms = √(3P/ρ) = √(3PV/M) as ρ = (M/V)

Vrms ∝ √(P/M)

∴ (V1/V2) = √{(P1/P2) × (M2/M1)}

Given: P1 = P0

V2 = 2V1

M2 = (M1/2)

∴ (V1/2V1) = √{(P0/P2) × (M1/2M1)}

(1/2) = √{(P0/P2) × (1/2)}

(1/4) = (P0/2 P2)

P2 = 2 P0