In an adiabatic process, `R = (2)/(3) C_(v)`. The pressure of the gas will be proportional to:

Options

A. `T^(5//3)`
B. `T^(5//2)`
C. `T^(5//4)`
D. `T^(5//6)`

Answer

B

Explanation

`R = (2)/(3) C_(v)`
We know, `C_(P) - C_(V ) = R`
or `gamma - 1 = (R )/(C_(V))`
or `R = C_(V) (gamma - 1)`
Comparing `gamma = 5//3`
`P^(1 - gamma) T^(gamma) =` constant = `K`
or `P prop T^((gamma//gamma -))` Given `gamma = 5//3`
`gamma//(gamma - 1) = 5//2` so, `P prop T^(5//2)`