Water in a piston cylinder assembly undergoes a cycle consis

Water in a piston cylinder assembly undergoes a cycle consisting of the following three processes. The initial pressure and specific volume are 300 kPa and 0.52 m^3/kg, respectively 1 - 2: constant pressure heating to a specific volume of 0.8 m^3/kg. 2 - 3: adiabatic compression to a pressure of 500 kPa. 3 - 1: constant volume cooling to the initial conditions Fix each state by determining the phase, temperature, quality (if necessary) and specific internal energy each state. Sketch the cycle on p-v and T-v diagrams with respect to the vapor dome. Determine the specific work and specific heat transfer for each process. What is the net specific heat transfer and the net specific work for the cycle?

Solution

a)From water properties at 300 kpa and 0.52m^3/kg we get T1=134degC, quality x1=0.858,internal energy u1=2260kj/kg,Entropy s1=6.24kj/kg-k

From water properties at P2=P1=300kpa and v2=0.8m^3/kg,we ger t2=252deg c,quality=superheated vapor,u2=2730kj/kg,s2=7.53kj/kg-k

From water properties at p3=500kpa and v3=v1=.52m^3/kg we get t3=297deg c,quality=superheated vapor,u3=2800 kj/kg,s3=7.45kj/kg-k

C) specific work w12=P×(v2-v1)=300×(.8-.52)=84kj/kg

Heat transfer q12=w12+(u2-u1)=84+(2730-2260)=554kj/kg

q23=0(since adiabatic)w23=q23-(u3-u2)=0-(2800-2730)=-70kj/kg

W31=0(since constant volume process)

q31=w31+(u1-u3)=0+(2260-2800)=-540kj/kg

D)Net heat transfer=q12+q23+q31=554+0-540=14 kj/kg

Net work=w12+w23+w31=84-70+0=14kj/kg