In an adiabatic change, the pressure and temperature of a monoatomic gas are related with relation as `P prop T^(C )`, Where `C` is equal to:

Options

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

Answer

B

Explanation

`gamma = 1+(2)/(f)`
`rArr gamma` for mono atomic gas `= 1+(2)/(3)=(5)/(3)`
For adiabatic relation `(P^(gamma-1))/(T^(gamma))` = const,
`P prop T^((gamma)/(gamma-1)) rArr P prop T^((5)/(3)xx(3)/(2))`
`therefore T^(C )=T^((5)/(2))rArr C = (5)/(2)`.