In 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

Coefficient of volume expansion `alpha_(V)=(dV)/(VdT)`
`PT^(2)=K and PV=nRT`
`(T^(2))/(V)=(K)/(nRT)rArr (KV)/(nR)=T^(2)`
Differentiating.`" "(T^(3))/(V)dV=3T^(2)dTrArr alpha_(V)=(dV)/(dT)=(3)/(T)`