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Please help me with this problem.

# A fixed mass of gas at constant pressure occupies a volume V. The gas undergoes a rise in temperature so that the root mean squared velocity(c) of the molecule is doubled. What is the new volume?

I solved it in the following way:-

Let V1 be the initial volume & V2 be the final volume. Assuming the pressure to be constant,

c = (3PV1/M)^1/2 --------- (1)

2c = (3PV2/M)^1/2 --------- (2)

Dividing equation (1) by (2) we get,

½ = (V1/V2)^1/2

Squaring on both sides we get,

¼ = (V1/V2)

V2 = 4V1

But the answer given in my book is V2 = V1/[(2)^1/2] read as V1 divided by root 2.Here the symbol ^ represents power.