How Is Power Calculated in a Turbine with Heat Transfer?

[paul1234]

Homework Statement

Hey Guys,

Steam enters a turbine with a velocity 120 m/s at 600°C and 600kPa. The steam leaves the turbine as saturated vapor at 200 kPa with a velocity of 180 m/s. heat is transferred from the turbine to the surroundings in the amount of 30 kJ for every kilogram of steam flowing through the turbine. The mass flow rate of steam through the turbine is 20 kg/s (1 kJ/kg = 1000 m2/s2)
Find the work and power.

Homework Equations

Ef-Ei=W-Q

 

[Valkarie]

W=m(h2-h1)P=W/tThe Attempt at a SolutionWe know that W=m(h2-h1). We also know that m= 20 kg/s. W=(20 kg/s)(h2-h1) We need to find h2 and h1. To find h2, we will use steam tables. At 600°C, we can see that the specific enthalpy of the steam is 2911.5 kJ/kg. At 200 kPa, we can see that the specific enthalpy of the steam is 2729.9 kJ/kg. Therefore, h2=2729.9 kJ/kg and h1=2911.5 kJ/kg Substituting these values into the equation, we get: W=(20 kg/s)(2729.9 kJ/kg - 2911.5 kJ/kg) W=-181.6 kJ/s We know that Q=30 kJ/kg and Ef-Ei=W-Q Therefore, Ef-Ei=-211.6 kJ/s We can then find the Power, P=W/t P=-181.6 kJ/s / 1 s P=-181.6 kJ/s