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

Options

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

Answer

C

Explanation

(C) `PT^2=constant (given)`
Also for an ideal gas `(PV)/T=constt`
From the above two equations, after eliminatig P.
`V/T^3=constt rArr V=kT^3 where k=constant`
`rArr(dV)/V=3(dT)/T`
`rArrdv=(3/T)VdT……(i)`
We know that change in volume due to thermal
expansion is given by `dV=VgammadT......(ii)`
Where gamma=coefficient of volume expansion.
From (i) and (ii)
`VgammadT=(3/T)VdT rArr gamma=3/T`