The relation between pressure and temperature of a monoatomic gas in an adiabatic process is `P prop T^(-C)`, where C = ____

Options

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

Answer

A

Explanation

The relation between pressure and temperature in an adiabatic process,
`P.T^(gamma/(1-gamma))` =constant
`therefore P prop T^((1-gamma)/gamma)`, comparing it with `P prop T^(-C)`
`therefore -C=(1-gamma)/gamma`
`therefore C=(gamma-1)/gamma`
For monoatomic gas `gamma=5/3`
`therefore C=(5/3-1)/(5/3)=(2/3)/(5/3)`
`therefore C=2/5`