Air initially exists in an unconstrained pistoncylinder asse

Air initially exists in an unconstrained piston-cylinder assembly at 200 kPa, 20 degree C, and 0.02 m^3. The air is heated until the volume is doubled. Determine the following: Mass of air in the piston-cylinder (kg). Pressure of the air at the end of the process (kPa). Temperature of the air at the end of the process (K). Boundary work (kJ). Heat transfer (kJ).

Solution

given that pressure p1=200 kpa

temp=20 c = 293 k

volume v1=0.02, v2=0.04

work done w = mcpdt

work done= p1v1=200*1000*0.02=4 kw

The nominal values used for air at 300 K are C_P = 1.00 kJ/kg.K, C_v = 0.718 kJ/kg.K,, and k = 1.4

so w = p1v1 = mcpdt

mcpdt= m*1kj/kg.k *293

m= 4000/293*1000=0.1365kg

pressure pv^k =c

so p1v1^k = p2v2^k

^{200*0.02 ^1.4 = p2*0.04^1.4}

^{p2= 75.78kpa}

PV/T = Constant

p1v1/t1 = p2v2/t2

200*0.02/293 = 75.78*0.04/t2

t2=222.03 kelvins

boundary work = m cp dt = 0.1365*1*71= 9.69kw ---negative work ---since work on the system

heat transfer q - w = internal energy

q= w= 9.69 kj