20 Due 4/15

1. You want to cool your cryogenics experiment by pumping pressurized liquid nitrogen through it. What is the power needed for a reversible pump that pressurizes 20 g/s of liquid nitrogen at 77.3 K from 200 kPa to 1MPa? Make appropriate approximations. Note: Under standard atmospheric pressure, liquid nitrogen boils at 77.3 K, and then has a specific volume of the liquid equal to 0.001240 m$\POW9,{3}$/kg and of the vapor 0.21639 m$\POW9,{3}$/kg.

2. A typical specific heat ratio for the hot combustion gases entering the turbine of a jet engine is 1.25. For the gas constant, just use the one for air. Assume that the gases enter the turbine at 640 kPa and 927$\POW9,{\circ}$C, and exit at the ambient pressure of 100 kPa at a rate of 2 kg/s. Also assume that the specific heat ratio is constant going through the turbine, and that the turbine is adiabatic and reversible. Find the exit temperature, power, and heat flow. Do not compute any volumes, specific or not, when solving this question.

3. An reversible isobaric heat exchanger heats a stream of carbon dioxide at 100 kPa from 300 to 500 K. It takes in heat from a 600 K reservoir. Find the work required, the heat taken from the reservoir, and the overall entropy generation.

4. A 0.25 kg/s stream of oxygen at 200 kPa and 17$\POW9,{\circ}$C and a separate 0.6 kg/s stream of nitrogen at 150 kPa and 500 K enter an insulated coflowing heat exchanger. There is heat conduction through the pipe wall separating the oxygen flow from the surrounding nitrogen flow, so the oxygen will heat up and the nitrogen cool down. The heat exchanger is long enough that oxygen and nitrogen come out with the same temperature. Determine that exit temperature and find the entropy generated by the process. Use constant specific heats from table A-2(a), not A-17--A-25. Make a typical approximation for heat exchangers for each stream.