The polytropic process is also known as the general law for the expansion and compression of gases and is given by the relation:
![](data:image/png;base64,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)
where n is a polytropic index, which may have any value from zero to infinity, depending upon the manner, in which the expansion or compression has taken place. The various equations for polytropic process may be expressed by changing the index n for Ɣ in the adiabatic process.
The heat absorbed or rejected during the polytropic process is given by
![](data:image/png;base64,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)
Notes:
(a) When n is less than Ɣ , then heat is absorbed by the gas.
(b) When n is greater than Ɣ , then heat is rejected by the gas.
(c) The polytropic index (n) is given by
where n is a polytropic index, which may have any value from zero to infinity, depending upon the manner, in which the expansion or compression has taken place. The various equations for polytropic process may be expressed by changing the index n for Ɣ in the adiabatic process.
The heat absorbed or rejected during the polytropic process is given by
Notes:
(a) When n is less than Ɣ , then heat is absorbed by the gas.
(b) When n is greater than Ɣ , then heat is rejected by the gas.
(c) The polytropic index (n) is given by
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