A steady flow of air at the rate M? will enter a steady-state device at T 1

Question:

A steady flow of air at the rate M? will enter a steady-state device at T₁, P₁ and emerge at T₂, P₂. The device requires shaft power W? and is cooled by heat transfer at the rate Q?₀ to the environment at T₀.

The specifications are that T_1?= T₂ = T₀ and P₂ > P₁.Starting from basic principles, and using the ideal gas equations of state, derive an expression for the minimum W? required by this device, in terms of M?, T₀, the pressure ratio ?_P?= P₂/P₁, and constants for the gas.