The pressure of a given mass of a gas changes from 200Nm−² to 120Nm−² while the temperature drops from 127°C to -73°C. The ratio of the final volume to the initial volume is?

A. 2 : 5
B. 5 : 4
C. 5 : 2
D. 4 : 5

Correct Answer:

Option B – 5 : 4

Explanation

P1 = 300Nm^-2; P2 = 120Nm^-2
T1 = 127 + 273; T2 = -73 + 273
= 400K; = 200K

Let the initial volume V1; and the final volume = V2

∴ P1V1/T1 = P2V2/T2
P1V1T2 = P2V2T1
∴ V2/V1 = P1T2/P2T1
∴ V2/V1 = (300 x 200)/(120 x 400) = 5/4

∴ V2 : V1 = 5 : 4