Question

A piston/cylinder system initially holds air at a pressure of 5.5 psig in a volume of 1 ft^3. The ambient pressure oitside the cylinder is 14.5 psia. The cylinder sits in an insulated bath containing 60 lbm of water. The contents are compressed to 100 psia. Intially they both have a temp of 50 F. After compression both air and water have a final temp of 51 F

a) Find the mass of air in cylinder in lbm

b) Hiw much work was supplied in . compression process? in BTU

Answer 1

given

piston / cylinder system

Pi = 5.5 psig = 20 psia

Vi = 1 ft^3

Po = 14.5 psia

cylinder is in an insulated bath containing

m = 60 lbm water

Pf = 100 psia

Ti = 50 F = 10

Tf = 51 F = 10.556

a. mass of air in cylinder = m

for adiabatic comperssion

PiVi^gamma = PfVf^gamma

gamma = 1.4

hence

Vf = 0.316763921 ft^3

work done on the gas = PiVi^gamma(Vf^(1-gamma) - Vi^(1-gamma))/(gamma - 1) = 29.19098 BTU

Work done = increase in internal energy of the gas + the water

also

PfVf = nRTf

689476*0.0089697553568374 = n*8.31*(273.16 + 10.556)

n = 2.62310 moles of air

molar mas sof air = 28.97 g/mol

hence m = 75.9912161091 g

b. Work supplied, from part a is 29.19098 BTU