An insulated rigid tank on a spacecraft contains nitrogen at 2000 psig and 70 o F.

An insulated rigid tank on a spacecraft contains nitrogen at 2000 psig and 70 oF. It is desired to discharge the tank isothermally to supply constant temperature nitrogen to the attitude control thrusts. This can be done if a portion of the discharged nitrogen is recycled back to the tank through a heater and compressor as shown in the schematic. Assuming nitrogen to be an ideal gas and ignoring any changes in tank or flow stream kinetic and potential energies, determine a) an expression for the ratio of recycled mass flow rate (m R) to discharge mass flow rate (m D) so that the temperature of the nitrogen in the tank (TT) is constant in time, and b) the value of m R/ m D and QH for TR = 200 oF, TT = 70 oF, m R =0.5 lbm/s, and Wc =3.0 hp.