Steam flows steadily through a turbine at a rate of 420 kg/min. The enthalpy of the steam decreases by 600 kJ/kg as it flows steadily through the turbine. If the power generated by the turbine is 4 MW, determine the rate of heat loss from the steam turbine [kW).

the rate of heat loss from the steam turbine is Q = 200 kW

Explanation:

From the first law of thermodynamics applied to open systems

Q-W₀ = F * (ΔH + ΔK + ΔV)

where

Q = heat loss

W₀ = power generated by the turbine

F = mass flow

ΔH = enthalpy change

ΔK = kinetic energy change

ΔV = potencial energy change

If we neglect the changes in potential and kinetic energy compared with the change in enthalpy, then

Q-W₀ = F*ΔH

Q = F*ΔH + W₀

replacing values

Q = F*ΔH + W₀ = 420 kg/min * (-600 kJ/kg) * 1 min/60 s * 1 MW/1000 kW + 4 MW = - 0.2 MW = - 200 kW (negative sign comes from outflow of energy)