Question

A fixed mass of gas at constant pressure occupies a volume ‘V’. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecule is doubled. The new volume will be ______.

Options

• `V/2`

• `V/sqrt 2`

• 2 V

• 4 V

Answer 1

A fixed mass of gas at constant pressure occupies a volume ‘V’. The gas undergoes a rise in temperature so that the r.m.s. velocity of the molecule is doubled. The new volume will be 4 V.

Explanation:

V_rms = `sqrt ((3 RT)/M)`

= `sqrt ((3 PV)/M)`    ...(∵ PV = RT)

∴ V_rms ∝ `sqrt V`

∴ `(V_"rms")_1/(V_"rms")_2 = sqrt (V_1/V_2)`

∴ `sqrt (V_1/V_2) = 1/2`    ...(Given: (V_rms)₂ = 2(V_rms)₁)

∴ V₂ 

= 4V₁