Heat Engine, Entropy, and the Second Law of Thermodynamics

7-1

A particular engine has a power output of 5.00 kW and an efficiency of 25.0 %. Assuming that the engine expels 8000 J of energy in each cycle, find (a) the energy absorbed in each cycle and (b) the time for each cycle.

7-2

One mole of an ideal monatomic gas is used as the working substance of an engine that operates on the cycle shown in Fig. 11. Calculate (a) the work done per cycle, (b) the heat added per cycle during the expansion stroke $abc$, and (c) the engine efficiency. (d) What is the Carnot efficiency of an engine operating between the highest and lowest temperatures present in the cycle? How does this compare to the efficiency calculated in (c)? Assume that $P= 2P_0$, $V=2V_0$, $P_0 = 1.01\times 10^5 \rm Pa$, and $V_0= 0.0225 \rm m^3$.

Figure 11: Prob 7-2

7-3

In a cylinder of an automobile engine just after combustion, the gas is confined to a volume of $50.0  \rm cm^3$ and has an initial pressure of $3.00 \times 10^6  \rm Pa$. The piston moves outward to a final volume of $300  \rm cm^3$, and the gas expands without energy loss by heat. (a) If $\gamma = 1.40$ for the gas, what is the final pressure? (b) How much work is done by the gas in expanding?

7-4

A 1.60-L gasoline engine with a compression ratio of 6.20 has a power output of 102 hp. Assuming that the engine operates in an idealised Otto cycle, find the energy absorbed and exhausted each second. Assume that the fuel-air mixture behaves like an ideal gas, with $\gamma = 1.40$.

7-5

To make ice, a freezer extracts 42 kcal of heat at $-12  \rm ^oC$. The freezer has a coefficient of performance of 5.7. The room temperature is $26 \rm ^o C$. (a) How much heat was delivered to the room? (b) How much work was required to run the freezer?