A kerosene fuelled gas turbine operates with a fuel mass flow rate and air mass

Question

A kerosene fuelled gas turbine operates with a fuel mass flow rate and air
mass flow rate of 5 kg/s and 300 kg/s respectively. Air enters the compressor
and methane enters the combustor at the standard reference state (298 K,
101.325 kPa). The gas turbine produces 100 MW of power, and loses 1 MW
of heat to the surrounding environment. Applying the steady flow energy
equation to an appropriate control volume, determine the final temperature of
the exhaust gas leaving the gas turbine.

The balanced reaction equation for this problem is:
5.00 kg/s kerosene + 300 kg/s air ? 15.401 kg/s CO2 + 7.209 kg/s H2O +
52.290 kg/s O2 + 230.100 kg/s N2
The lower calorific value (LCV) of kerosene at 25degrees Celcius is 43.74 MJ/kg.
Values of cp: CO2 Dry air O2 N2 Steam
(kJ/kg.K) 1.10 1.08 1.02 1.10 2.10

Explanation / Answer

From energy balance on control volume Energy of reactants = output + losses + energy of products 5 * 43.74* 1000 + 0 (refernce state ) = 100* 1000+ 1000+ 15.401* 1.10* T + 7.209 * 2.1 * T+ 55.29* 1.02 * T + 230.1* 1.1 * T So T = 344.57 K So T2 - T1 = 344.57 T2= 642.57 K

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