A process, in which the temperature of the working substance remains constant during its expansion or compression, is called a constant temperature process or isothermal process. This will happen when the working substance remains in a perfect thermal contact with the surroundings, so that the heat 'sucked in' or 'squeezed out' is compensated exactly for the mechanical work done by, or on the gas respectively. It is thus obvious that in an isothermal process:
1. there is no change in temperature, and
2. there is no change in internal energy.
We know that
Q1-2 = dU + W1-2 = W1-2
Hence during isothermal expansion of a gas,
Heat added = Work done by the gas
Similarly, during isothermal compression of a gas,
Heat subtracted = Work done on the gas
A little consideration will show that the isothermal process is governed by Boyle's law. Thus the isothermal equation of a perfect gas is pv = Constant.
Now consider a certain quantity of a perfect gas being expanded isothermally, which is shown by the curve 1-2 in Fig. 5.3.
![](data:image/png;base64,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)
Let
v1 = Initial volume of gas,
p1 = Initial pressure of gas,
v2 = Final volume of gas, and
p2 = Final pressure of gas.
The workdone during isothermal expansion is given by
W1-2 = Area under the curve 1-2
![](data:image/png;base64,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)
In general,
![](data:image/png;base64,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)
where r is the expansion ratio (when gas is heated) or compression ratio (when gas is cooled).
Notes:
(a) Expansion ratio (r) = (Volume at the end of expansion)/(Volume at the beginning of expansion)
(b) Compression ratio (r) = (Volume at the beginning of compression)/(Volume at the end of compression)
1. there is no change in temperature, and
2. there is no change in internal energy.
We know that
Q1-2 = dU + W1-2 = W1-2
Hence during isothermal expansion of a gas,
Heat added = Work done by the gas
Similarly, during isothermal compression of a gas,
Heat subtracted = Work done on the gas
A little consideration will show that the isothermal process is governed by Boyle's law. Thus the isothermal equation of a perfect gas is pv = Constant.
Now consider a certain quantity of a perfect gas being expanded isothermally, which is shown by the curve 1-2 in Fig. 5.3.
Let
v1 = Initial volume of gas,
p1 = Initial pressure of gas,
v2 = Final volume of gas, and
p2 = Final pressure of gas.
The workdone during isothermal expansion is given by
W1-2 = Area under the curve 1-2
In general,
where r is the expansion ratio (when gas is heated) or compression ratio (when gas is cooled).
Notes:
(a) Expansion ratio (r) = (Volume at the end of expansion)/(Volume at the beginning of expansion)
(b) Compression ratio (r) = (Volume at the beginning of compression)/(Volume at the end of compression)
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