Is $p\cdot V^γ= \mathrm{const.}$ valid for only adiabatic reversible process and not for adiabatic irreversible process if not why?
Today I was doing an objective question as mentioned above and chose option "any adiabatic process" but the ans was "only reversible adiabatic process" but i couldn't understand why. All i know is that path followed by both process will be different but how will it affect the adiabatic equation i.e $p\cdot V^γ= \mathrm{const}$.
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An adiabatic and reversible process (i.e. isentropic) for ideal gases can be described as follows1:
$p \cdot V^\gamma = \mathrm{const.}$
Here $\gamma$ is the heat capacity ratio. Other processes can be described by changing the exponent. The equation for a polytropic process is:
$p \cdot V^n= \mathrm{const.}$
For $n=1$ this equation describes a isothermal process and for values greater $\gamma$ this equation can be used to describe irreversible processes.