I know that every adiabatic reversible process is an isentropic process.
Can a process be isentropic but still not reversible adiabatic?
Please provide me some examples.
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Reversibility implies that the entropy change of the universe is 0. An isentropic process need not necessarily be reversible, provided that the entropy of the surroundings is increased.
For an irreversible process, heat can be removed from the system in order to make it isentropic (since $dQ < TdS$. As heat is removed, you will have an isentropic process that is both irreversible and adiabatic. As the surroundings receive the heat, the entropy change of the universe is positive, which agrees with the fact that the process is irreversible.
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$\begingroup$ while deriving the expression for entropy my lecturer used two different operators one in δ and another is d. He also said that since Q and W are path functions he used δ and since entropy is a state function he used d operator can you please tell me the difference...? $\endgroup$ Commented Oct 1, 2014 at 14:00
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$\begingroup$ Usually, in thermodynamics (and multivariate calculus) $dz$ denotes an exact differential and $\delta z$ denotes an inexact differential. An exact differential means that it can be expressed in the form of $dz = Adx + Bdy$ where $A = \partial{z}/\partial{x}$ and $B = \partial{z}/\partial{y}$. An exact differential means that it is path independent. $\endgroup$– t.cCommented Oct 1, 2014 at 14:38