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

Answer

C

Explanation

Key Idea: Poisson's equation for adiabatic process is given by
pV=constant
For adiabatic process, Poisson's equation is given by
` pV^(gamma)="constant"....(i)`
Ideal gas relation is
pV=Rt
`Rightarrow V=(RT)/(p)......(ii)`
`p((RT)/(P))="constant"`
`Rightarrow (T^(gamma))/(p^(gamma-1))="constant"....(iii)`
Where `gamma` is the ration of specific heats of the gas Given `p alpha T^(C).....(iv)`
On comparing with Eqs. (iii) we have
`C=(gamma)/(gamma-1)`
For a monoatomic gas `gamma=(5)/(3)`
We have
`C=((5)/(3))/((5)/(3)-1)=(5)/(2)`