Air as an ideal gas I temperature is compressed from a state

Air as an ideal gas I temperature is compressed from a state where the pressure is 0.1 MPa and the temperature is 27 degreeC. to a state where the pressure is 0.5 MPa and the temperature is 207 degreeC. Can this process occur adiabatically? If yes, determine the work per unit mass of air, in KJ/Kg, for an adiabatic process between these States. If no, determine the direction of heat transfer.

Solution

By using ideal gas equation for air PV = mRT , we get V1 and V2 as mass = 1kg and t1 = 300K and t2 = 480K and pressure P₁ = 0.1 Mpa and P₂ = 0.5 Mpa and then checking adiabatic condition P₁*V₁^x = P₂V₂^x (by using V1 and V2 from ideal gas equation) we get L.H.S = R.H.S. Hence process is adiabatic.

Work done per unit mass for adiabatic process is P₁V₁ - P₂V₂ / x-1 = 129.15 KJ/Kg .

Here R = .287KJ/kg.K and x_air = 1.4