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)=`constant
`((nRT)/(V))T^(2)=`constant
`T^(3)V^(1)=`constant
Differentiating the equation, we get
`(3T^(3))/(V)dT-(T^(3))/(V(3))dV=0`
`3dT=(T)/(V)dV`
From the equation, `dV=VgammadT`
`gamma=` coefficient of volume expansion of gas `=dV//VdT` .
From Eq. (i) , `gamma=(dV)/(VdT)=(3)/(T)`