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-1), given `gamma = 5/3`
`(gamma)/((gamma-1)) = 5/2`
So, `P prop T^(5//2)`.