A process, in which the working substance neither receives nor gives out heat to its surroundings, during its expansion or compression is called an adiabatic process or isentropic process. This will happen when the working substance remains thermally insulated, so that no heat enters or leaves it during the process. It is thus obvious, that in an adiabatic process:
1. No heat leaves or enters the gas,
2. The temperature of the gas changes, as the work is done at the cost of internal energy, and
3. The change in internal energy is equal to the work done.
We know that
![](data:image/png;base64,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)
Minus sign indicates, that for increase in internal energy, work must be done on the gas (i.e. -ve work must be done by the gas). Similarly, for decrease in internal energy, work must be done by the gas.
* A frictionless adiabatic process is known as Isentropic process (or constant entropy process).
Now consider a certain quantity of a perfect gas being expanded adiabatically which is shown by the curve 1-2 in Fig. 5.4.
![](data:image/png;base64,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)
Let
v1 = Initial volume of gas,
p 1 = Initial pressure of gas,
v2 = Final volume of gas, and
p2 = Final pressure of gas.
The workdone during adiabatic process is given by
(For expansion)
![](data:image/png;base64,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)
(For compression)
![](data:image/png;base64,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)
Notes:
(a) For adiabatic process,
![](data:image/png;base64,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)
(b) Since p1v1 = mRT1 and p2v2 = mRT2, therefore the above equation may be written as
1. No heat leaves or enters the gas,
2. The temperature of the gas changes, as the work is done at the cost of internal energy, and
3. The change in internal energy is equal to the work done.
We know that
Minus sign indicates, that for increase in internal energy, work must be done on the gas (i.e. -ve work must be done by the gas). Similarly, for decrease in internal energy, work must be done by the gas.
* A frictionless adiabatic process is known as Isentropic process (or constant entropy process).
Now consider a certain quantity of a perfect gas being expanded adiabatically which is shown by the curve 1-2 in Fig. 5.4.
Let
v1 = Initial volume of gas,
p 1 = Initial pressure of gas,
v2 = Final volume of gas, and
p2 = Final pressure of gas.
The workdone during adiabatic process is given by
(For expansion)
(For compression)
Notes:
(a) For adiabatic process,
(b) Since p1v1 = mRT1 and p2v2 = mRT2, therefore the above equation may be written as
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