Problem 1: Consider the ideal Brayton cycle model for an aircraft engine as shown in the diagram below. The compressor, turbine, and nozzle are all assumed to operate with an isentropic efficiency of 100%. The process fluid is air that can be modeled as an ideal gas with constant specific heats. The following steady-state conditions for the operation of the cycle are known:
$P_1 = 75 \text{ kPa}$, $T_1 = 300 \text{ K}$, $P_2 = 2200 \text{ kPa}$, $T_3 = 1000 \text{ K}$, $P_4 = 75 \text{ kPa}$, $\dot{m} = 8.5 \text{ kg/s}$, $c_p = 1.18 \text{ kJ/kg-K}$
Determine:
(A) The specific heat ratio, $k$
(B) The temperature at state 2, $T_2$
(C) The pressure at state 3, $P_3$
(D) The temperature at state 4, $T_4$