Discussion
The stagnation temperatures at the inlet and exit of a combustion chamber are 600 K and 1200 K, respectively. If the heating value of the fuel is 44 MJ/kg and specific heat at constant pressure for air and hot gases are 1.005 kJ/kg.K and 1.147 kJ/kg.K respectively, the fuel-to-air ratio is
Answer: B
The fuel-to-air ratio is 0.018.
An energy balance on the combustor, per kg of air, with fuel-to-air ratio f: the heat released by the fuel raises the air from its inlet enthalpy to the exit enthalpy of \((1 + f)\) kg of hot gas.
\[ \begin{aligned} f\,Q &= (1 + f)c_{pg}T_{02} - c_{pa}T_{01} \\ 44000f &= 1376.4(1 + f) - 603 \\ 42623.6f &= 773.4 \\ f &= 0.0181 \end{aligned} \]
with \(c_{pg}T_{02} = 1.147 \times 1200 = 1376.4\) kJ/kg and \(c_{pa}T_{01} = 1.005 \times 600 = 603\) kJ/kg. The other options are the same digits shifted by factors of ten; a real gas turbine combustor runs at about 0.02, so 0.18 and 1.18 are far too rich and 0.0018 far too lean.
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