Problem 26.31 (RhK) We have to show that a Carnot cycle, plotted on an absolute temperature versus entropy (TS) diagram, graphs as a rectangle. For the Carnot cycle shown in the figure, (b) we have to calculate the heat that enters; and (c) the work done on the system.
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Solution: Click For PDF Version We will show that a Carnot cycle when plotted on a T-S plane has a rectangular graph. The Carnot cycle consists of two adiabatic processes and two isothermal processes. In an adiabatic process, as the system is thermally insulated, there is no exchange of heat and as the process is reversible there is no change in entropy.
In isothermal
processes during the expansion phase an amount of heat
Therefore,
From the discussion above we note that the graph of the Carnot cycle on a T-S plane is a rectangle.
(b)
For the
Carnot engine shown in the figure the amount of heat that enters the
system at temperature
is
The amount of
heat that leaves the system at
Therefore, the work done by the system
And the work done on the system will be -75 J.
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is absorbed by the working substance during its contact with the
high temperature heat reservoir, which is at temperature
.
Therefore, the entropy of the system increases by an amount equal to
.
And during the compression phase an amount of heat
is released to the cold heat reservoir, which is at temperature
.
Therefore, the entropy of the working substance gets decreased by an
amount
.
As the Carnot cycle is a reversible thermodynamic process, the
change in entropy of the system over one cycle is zero.
is
