Air (14.5 lb) undergoes a polytropic process in a closed system from p1 = 80 lbf/in2, υ1 = 4 ft3/lb to a final state where p2 = 20 lbf/in2, υ2 = 11 ft3/lb. determine the amount of energy transfer by work (in btu) for the process

The energy transfer in terms of work has the equation:

W = mΔ (PV)

To be consistent with units, let's convert them first as follows:

P₁ = 80 lbf/in² * (1 ft/12 in) ² = 5/9 lbf/ft²

P₂ = 20 lbf/in² * (1 ft/12 in) ² = 5/36 lbf/ft²

V₁ = 4 ft³/lbm

V₂ = 11 ft³/lbm

W = m (P₂V₂ - P₁V₁)

W = (14.5 lbm) [ (5/36 lbf/ft²) (4 ft³/lbm) - (5/9 lbf/ft²) (11 lbm/ft³) ]

W = - 80.556 ft·lbf

In 1 Btu, there is 779 ft·lbf. Thus, work in Btu is:

W = - 80.556 ft·lbf (1 Btu/779 ft·lbf)

W = - 0.1034 BTU