An ideal gas is initiaily at temperature T and volumoeV. lts volume is increased by `Delta V` due to an increase in temperature `Delta T`, pressure remaining constant. The quantity `k = AV//(V Delta T)` varies with temperature as:

Options

A.
B.
C.
D.

Answer

C

Explanation

For ideal gas `PV=nRT`
At const. pressure.
`Pdv =nRdT`
`(dV)/(dT) =(nR)/(P)`
`AB.P =(nRT)/(V)`
`therefore (dV)/(dT) =(nR)/(nRT) cdot V`
`rArr (1)/(V) cdot (dV)/(dT) =(1)/(T)`
`rArr k=(1)/(T) rArr k prop (1)/(T)`
Thus, correct choice is (c ).