For an adiabatic process of an ideal monatomic gas the pressure and the temperature are related as `p prop T^(C )`. Find out the value of C.

Explanation

For an adiabatic process of an ideal gas,
`p^(1-gamma) T^(gamma) or , p = (kT^(-gamma))^(1/(1-gamma)) = k^(1/(1-gamma))T^(gamma/(gamma-1))`
`:. p prop T^(gamma/(gamma-1))`
As `p prop T^(C ), C = (gamma)/(gamma-1)`
For a monoatomic gas, `gamma = 5/3`
So, `C = (5/3)/(5/3-1) = 5/2`.