In a Carnot cycle, the isothermal expansion of an ideal gas takes place at 412 k and the isothermal compression at 297 K. During the expansion, 2090 J of heat energy are transferred to the gas. We have to determine (a) the work performed by the gas during the isothermal expansion, (b) the heat rejected from the gas during the isothermal compression; and (c) the work done on the gas during the isothermal compression.
|
Solution: Click For PDF Version In a Carnot engine cycle isothermal expansion of the gas takes place when the gas is in contact with the hot-reservoir. Therefore, the temperature of the hot-reservoir
And the isothermal compression takes place when the gas is in contact with the cold-reservoir. Therefore, the temperature of the cold-reservoir is
In a Carnot
engine the ratio of the heat absorbed from the hot-reservoir
Therefore, the heat rejected to the cold-reservoir that is during the isothermal compression will be
In an
isothermal process the internal energy of the gas remains unchanged.
Therefore, the work performed by the gas during the isothermal
expansion will be equal in magnitude to the heat absorbed
Similarly
during the isothermal compression, as heat is rejected to the
cold-reservoir and the internal energy of the gas remains constant,
amount of work done on the gas will be equal in magnitude to
|
and the heat rejected to the cold-reservoir
is determined by the temperatures
and
.
It is given by the relation
