The car engine has a
compression ratio of 8.0. The
molar specific heat ratio Ȗ is 1.4.
What is the theoretical engine
efficiency?
eice = 0.56 = 56%
21.10 - Heat pumps
Heat pump: A device that transfers heat from a
colder environment to a warmer one.
It may sound a bit odd to speak of transferring heat from a colder environment (say the
outdoors in the winter) to a warmer one (the interior of a building), but that is what heat
pumps do: They pump heat opposite to the direction it would normally flow.
Because heat pumps are more energy-efficient than typical furnaces, they are
becoming increasingly popular. An additional and very attractive benefit of heat pumps
is that in the summertime, they can be run in reverse to pump heat out of the cool
house into the warm outdoors, so the same appliance does double duty as a furnace
and as an air conditioner.
A heat pump can be thought of as a heat engine run in reverse. With a heat engine,
heat flows from the hot reservoir to the engine and then to the cold reservoir, and work
is done by the engine. With the pump, heat flows the opposite direction, from the cold
reservoir to the hot, and work must be done on the engine to accomplish this, since
heat does not flow spontaneously from cold to hot.
As mentioned above, a heat pump is in some ways analogous to an air conditioner (or a
refrigerator). In both cases, work is performed on the device, and it is used to transfer
heat in the direction opposite to the direction in which it spontaneously flows. However,
there is a difference between the two appliances. A heat pump moves heat from the
cold outdoors to a warmer indoors, with the purpose of further increasing the
temperature of the indoors. An air conditioner moves heat from indoors to outdoors,
with the purpose of further cooling the interior.
Efficiency is analyzed somewhat differently with heat pumps than it is with heat engines.
Recall that the maximum efficiency of a heat engine is determined by the ratio of the
cold and hot reservoir temperatures (e = 1 íTc/Th). When the temperature difference
is large, the ratio is small and the engine can be more efficient. In contrast, as you can
see from Equation 2, heat pumps work best when there is little temperature difference. The greater the difference, the harder the pump has to
work to transfer energy from the cold to the hot reservoir. For this reason, heat pumps are rated by the coefficient of performance (COP). You
see the definition of the coefficient of performance in Equation 1 on the right: It is the heat transferred to the hot reservoir divided by the work
done on the gas. Both the heat transfer and the work done on the engine are treated as positive quantities.
One way to think of the efficiency of a heat engine is as the ratio of “what you want” (work done) to “what you pay” (heat added). This applies to
the COP as well. The COP for a heat pump equals the ratio of “what you want” (heat flow) to “what you pay” (the work done on the gas). The
larger the COP, the more heat is transferred to the hot reservoir per unit of work done.
The maximum COP for a heat pump is determined, as for a heat engine, by the temperatures of the hot and cold reservoirs. An inequality that
Heat pump
Work moves heat from cold to hot
reservoir