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

Options

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

Answer

C

Explanation

`P^(T^(2))= "constant, "T^3 V^(-1) = "cconstant"`
Differentiating the equation, we get
`(3T^2)V dt - (T^3)/(V^2)dV =0`
`3dT = T/V dV " ...(i)"`
From the equation, `d V = V gamma dT`
`gamma =` coefficient of volume expansion of gas `=dV=VYdT.`. From Equation (i),` gamma = (dV)/(VdT) = 3/T`