the volume, the entropy increases in this case, therefore this process is irreversible.

Derivation of P-V relation for adiabatic compression and expansion

The definition of an adiabatic process is that heat transfer to the system is zero, Then, according to the first law of thermodynamics,

where is the change in the internal energy of the system and is work done by the system. Any work done must be done at the expense of internal energy since no heat is being supplied from the surroundings. Pressure-volume work

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