20 C11. Due 12/2

1. Consider a Stirling engine that uses helium as the working fluid. The helium enters the compression process at 100 kPa and 27$\POW9,{\circ}$C and is compressed to 600 kPa. After the compression it is isochorically heated to 1200 K.
   1. There is no regeneration, heat is exchanged with the surroundings. Compute the heat transfer in all four processes. From that find the specific work produced per kg passing through and the thermal efficiency. (Base the thermal efficiency on the work divided by the total heat put into the substance. Heat will come out by itself.)
   2. If ideal regeneration is added, what is the specific work and thermal efficiency then?

2. UNGRADED: A car engine has a compression ratio of 9. The heat added by the combustion of the fuel is 1800 kJ/kg. Typically, the air enters the cylinder at a vacuum compared to atmospheric, which produces bad “pumping losses.“ That reduces mpg. However, it can be minimized by switching to a high gear that keeps the engine rpm low. Then the air could be entering the cylinder with about atmospheric pressure, call it 85 kPa, and 300 K. Model the performance of such an engine using the ideal Otto cycle. Approximate the substance at all stages as air with constant specific heats. Take the given entrance conditions to apply at the start of the compression stroke.
   1. Find the thermal efficiency of the engine;
   2. From that, find the specfic work produced per kilogram air flowing through.
   3. Car engines are typically rated by the volume of air that they take in per cycle. Assume the intake volume is 2 L. The actual volume at the start of the cycle is greater than that by a factor $r_v/(r_v-1)$ because the minimum volume is not part of the stroke (the piston does not hit the end of the cylinder). Convert the volume to an intake mass using the given entrance conditions. Multiply the specific work by the mass to get the work per cycle.
   4. From that, compute the power produced at 2000 rpm (revolutions per minute; note that a cycle requires 2 revolutions.) Convert to metric horsepower. You may observe that a real engine stops somewhat short of ideal.
   5. Find the peak temperature and pressure in the engine. (Find the pressure and temperature before combustion first.) Note that the temperature presents a material problem.

3. A diesel engine has a compression ratio of 19:1. The heat transferred to the air during combustion is 1800 kJ/kg. At the beginning of the compression process the pressure is 100 kPa and the temperature is 27$\POW9,{\circ}$C. Determine, assuming the ideal cycle:
   1. The pressure and temperature at each point in the cycle.
   2. The thermal efficiency.
   3. The mean effective pressure.
   4. The engine is a 6 cylinder one, with a bore (cylinder diameter) of 10 cm and a stroke (piston motion) of 11 cm. It runs at 2000 rpm. What is the power produced?