Describe the Carnot cycle with the roles of all four processes involved
Outline the Carnot principle and its implications
Demonstrate the equivalence of the Carnot principle and the second law of thermodynamics
In the early 1820s, Sadi
Carnot (1786−1832), a French engineer, became interested in improving the efficiencies of practical heat engines. In 1824, his studies led him to propose a hypothetical working cycle with the highest possible efficiency between the same two reservoirs, known now as the
Carnot cycle . An engine operating in this cycle is called a
Carnot engine . The Carnot cycle is of special importance for a variety of reasons. At a practical level, this cycle represents a reversible model for the steam power plant and the refrigerator or heat pump. Yet, it is also very important theoretically, for it plays a major role in the development of another important statement of the second law of thermodynamics. Finally, because only two reservoirs are involved in its operation, it can be used along with the second law of thermodynamics to define an absolute temperature scale that is truly independent of any substance used for temperature measurement.
With an ideal gas as the working substance, the steps of the Carnot cycle, as represented by
[link] , are as follows.
Isothermal expansion. The gas is placed in thermal contact with a heat reservoir at a temperature
The gas absorbs heat
from the heat reservoir and is allowed to expand isothermally, doing work
Because the internal energy
of an ideal gas is a function of the temperature only, the change of the internal energy is zero, that is,
during this isothermal expansion. With the first law of thermodynamics,
we find that the heat absorbed by the gas is
Adiabatic expansion . The gas is thermally isolated and allowed to expand further, doing work
Because this expansion is adiabatic, the temperature of the gas falls—in this case, from
From
and the equation of state for an ideal gas,
, we have
so that
Isothermal compression . The gas is placed in thermal contact with a cold reservoir at temperature
and compressed isothermally. During this process, work
is done on the gas and it gives up heat
to the cold reservoir. The reasoning used in step 1 now yields
where
is the heat dumped to the cold reservoir by the gas.
Adiabatic compression . The gas is thermally isolated and returned to its initial state by compression. In this process, work
is done on the gas. Because the compression is adiabatic, the temperature of the gas rises—from
in this particular case. The reasoning of step 2 now gives
The total work done by the gas in the Carnot cycle is given by
Questions & Answers
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asegid
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Kamara
yes
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