An ideal gas is expanding such that `PT^2=constant.` The coefficient of volume expansion of the gas is-

Options

A. `(1)/(T)`
B. `(2)/(T)`
C. `(3)/(T)`
D. `(4)/(T)`

Answer

C

Explanation

`PT^(2) = C`
using `PV = nRT "in" PT^(2) = C`
`((nRT)/(V))T^(2) = C rArr T^(3) prop V`
Differentiating we get
`3(dT)/(T) = (dV)/(V)`
Coefficient of volume expansion
`(gamma) = (1)/(V) (dV)/(dT) = (3)/(T)`