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. `3/5`
D. `5/2`

Answer

D

Explanation

For adiabatic process
`PV^(gamma)` constant ..(i)
We have ideal gas relation , `PV=RT`
`implies V = (RT)/(P) `...(ii)
From equ. (i) and (ii) we get
`P((RT)/(P))^(gamma)` = constant
`implies (T^(gamma))/(P^(gamma-1)) = consta nt` ..(iii)
where `gamma` is adiabatic consta nt of the gas
Given `P prop T^(C)` ...(iv)
On comparing with eq, (iii) we have
`C = (gamma)/(gamma-1)`
For a monoatomic gas `gamma=5/3`
`:.` we have , `C = (5/3)/(5/3-1) = 5/2`.