13 C7a. Due 10/26

1. Some car driving 60 mph on the highway uses 8 L of fuel per hour. The heating value HV of the fuel is about 42.4 MJ/kg and the density is 750 kg/m$\POW9,{3}$. If the thermal efficiency of the engine is 25%, then what is the power available at the crankshaft axis in bhp?

2. For each of the cases below determine if the heat engine satisfies the first law, and if it does, if it satisfies the second law, and if it does, whether it is now a useful heat engine.

   $\dot Q_H$	$\dot Q_L$	$\dot W$	1st law?	2nd law?	useful?
   5	4	3
   5	3	2
   5	5	0
   5	0	5
   0	5	$-$5
   5	10	$-$5

3. For each of the cases below determine if the heat pump or refrigeration cycle satisfies the first law, and if it does, if it satisfies the second law, and if it does, whether it is now a useful heat pump or refrigeration cycle.

   $\dot Q_H$	$\dot Q_L$	$\dot W$	1st law?	2nd law?	useful HP?	useful RC?
   5	4	3
   5	3	2
   5	5	0
   5	0	5
   0	5	$-$5

   For the last case, in case you conclude that the second law is violated, state which of the two formulations is violated.

4. Water at 25$\POW9,{\circ}$C and 100 kPa enters an isobaric heat exchanger at a rate of 5 kg/s and is heated into saturated steam without droplets in it. The heat is provided by a heat pump with a coefficient of performance of 3. Determine the amount of power required by the heat pump.