During an adiabatic process , the pressure of a gas is proportional to the cube of its temperature . The value of `C_(I)//C_(v)` for that gas is

Options

A. `(7)/(5)`
B. `(4)/(5)`
C. `(5)/(3)`
D. `(3)/(2)`

Answer

D

Explanation

`implies P prop T^(3) ` (Given)
`implies P =K*T^(3)`
`implies P =K ((PV)/ R )^(3)` `(because PV = RT)`
`implies P = (K)/(R^(3))(PV)^(3)`
`therefore P^(2) V^(3) =K ` `(because (K)/(R^(3)) = Constant )`
Taking square root on both sides
`PV^(3//2) = K `
On comparing with the equation , PV = K
`therefore gamma = 3//2`