An ideal gas is expanding such that `PT^(2)= `constant. The coefficient of volume expansion of lthe gas is:

Options

A. `(1)/(T)`
B. `(2)/(T)`
C. `(3)/(T)`
D. `(4)/(7)`

Answer

C

Explanation

Given , `pT_(2)` constant
`therefore" " ((nRT)/(V))T^(2)` = constant
`or" " T^(3)V^(-1)` =constant
Differntiting the equation , we get
`(3T^(2))/(V).dT-(T^(3))/(T^(2)).dV=0" or "3.dT=(T)/(V).dT`
From the equation , `dT=Vgamma.dT`
`gamma` = coeffiecient of volume expansion of gas
`(dV)/(V.dT)`
`therefore" " gamma=(dV)/(V.dT)=(3)/(T)`