An uninsulated gas turbine receives air at 1000 kPa, 800oC, at a mass flow rate of 12.0 kg/s. The air exits at 100 kPa, 420oC. The turbine produces 4.10 MW of power.
(a) Determine the heat transfer rate for the turbine.
(b) Using your turbine model, plot the required heat transfer rate for exit temperatures varying between 400°C and 500°C, with the other conditions remaining the same.
(c) Using your turbine model and the original conditions, plot the variation in power produced as the heat transfer rate varies between 0.0 MW and -3.0 MW.
Given: P1 = 1000 kPa; T1 = 800°C; P2 = 100 kPa; T2 = 420°C; m?= 12.0 kg/s; W?=4.10 MW=4,100 kW; Air (Take State 1 as the inlet, State 2 as the outlet.)
Assume: For a turbine, assume steady-state, steady-flow, single-inlet, single-outlet flow, with ?KE = ?PE = 0
With these assumptions, the First Law for open systems reduces to Q??W?=m?(h2?h1)
As the temperature difference is rather large, we will consider the air to have variable specific heats:
h1 = 1129.83 kJ/kg
h2 = 705.75 kJ/kg
Solving: Q?=(12.0kgs)(705.75?1129.83)kJkg+4100 kW = -989 kW
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