A one mole of ideal gas goes through a process in which pressure p varies with volume V as `p =3-g((V)/(V_(0)))^(2)`, where, `V_(0)` is a constant. The maximum attainable temperature by the ideal gas during this process is
(all quantities are is SI units and Ris gas constant)

Options

A. `( 2V_0)/(3R)`
B. `(2 V_0)/(R )`
C. `( 3 V_0)/(2 R)`
D. `( 3V_0)/(R )`

Explanation

Given that , `P= 3 - g((V)/(V_0))^2`
We know `PV = nRT`
`rArr (3 - g ((V)/(V_0))^2 ) v = RT ( therefore N = 0) `
`rArr T = (3 v - g ((V)/(V_0))^2 )/(R )= (3V)/(R )- (g V^2 )/(RV_(0)^(2))`
For maximum value of T,
`(dT)/(dV) = 0 `
`rArr (dT)/(dV)= (3)/(R) - (g)/(RV_(0)^(2) ) (2V )`
`rArr (3)/(R ) - (2g V)/(RV_(0)^(2))= 0`
`rArr (3)/(R ) - (2gV)/( RV_(0)^(2))`
`V= (3V_(0)^(2))/(2g)`