# Homework Help: Finding Qdot for a Thermodynamic Rankine Cycle

1. Feb 16, 2012

### jaredogden

1. The problem statement, all variables and given/known data
Water is the working fluid in a Rankine cycle. Superheated vapor enters the turbine at 10 MPa, 480 °C condenser pressure = 6 kPa ηturbine = 80% ηpump = 70% determine a.) Qdot of the steam generator. b.) ηth c.) Qdot from the condenser to the cooling water.

2. Relevant equations
x2 = (s2 - sf)/(sg-sf)
Wturbine = Qdot/mdot = (h1 - h2
qin = Qdot/mdot = (h2 - h3 )
Wpump = Wdotpump/mdot = (h4 - h3)
qin = Qdot/mdot = (h1 - h4)

3. The attempt at a solution
s1 = s2 x3 = 0
T2 = T3 P4 = P1
P2 = P3 h3 = hf
s3 = s4

From the superheated water vapor table at 10 MPa and 480°C:
h1 = 3321.4 kJ/kg s1 = 6.5282 kJ/kg*K

From the saturated water mixture table at 6 kPa:
hf = 151.53 kJ/kg sg = 8.3304 kJ/kg*K
hg = 2567.4 kJ/kg sf = 0.5210 kJ/kg*K
hfg = 2415.9 kJ/kg vf = 1.0064x10-3 m3/kg

x2 = (6.5282 - 0.5210) [kJ/kg*K]/(8.3304 - 0.5210)[kJ/kg*K]
x2 = 0.7692

h2 = 151.53 kJ/kg + 0.7692(2415.9 kJ/kg)
h2 = 2009.84 kJ/kg
h3 = 151.53 kJ/kg
h4 = 151.53 kJ/kg + 1.0064x10-3 m3/kg(10 - 0.006)[MPa]
h4 = 161.59 kJ/kg