The gas-turbine cycle of a combined gas-steam power plant has a pressure ratio of $12 .$ Air enters the compressor at $310 \mathrm{K}$ and the turbine at $1400 \mathrm{K}$. The combustion gases leaving the gas turbine are used to heat the steam at $12.5 \mathrm{MPa}$ to $500^{\circ} \mathrm{C}$ in a heat exchanger. The combustion gases leave the heat exchanger at $247^{\circ} \mathrm{C}$. Steam expands in a high-pressure turbine to a pressure of $2.5 \mathrm{MPa}$ and is reheated in the combustion chamber to $550^{\circ} \mathrm{C}$ before it expands in a low-pressure turbine to $10 \mathrm{kPa} .$ The mass flow rate of steam is $12 \mathrm{kg} / \mathrm{s}$. Assuming all the compression and expansion processes to be isentropic, determine
(a) the mass flow rate of air in the gas-turbine cycle, ( $b$ ) the rate of total heat input, and ( $c$ ) the thermal efficiency of the combined cycle.