Internally Reversible and Isothermal Processes

[Ali Asadullah]

What are Internally reversible processes and why isothermal processes are reversible?
Also, Isothermal process are only internally reversible or they can be "externally" reversible?

 

[Andrew Mason]

What are Internally reversible processes and why isothermal processes are reversible?
Also, Isothermal process are only internally reversible or they can be "externally" reversible?

An "internally reversible" process is one for which the integral of dQ/T over the actual path between the beginning and end states of the system gives you the change in entropy of the system. (The change in entropy is the integral of dQ/T of the system over the reversible path between those two states).

A rapid expansion against an external pressure that is lower than the pressure of the gas (so the gas is not in equilibrium during the expansion) or a mixing of two different gases are internally irreversible processes.

Although a rapid non-quasi-static isothermal expansion of a gas is NOT internally reversible, an isothermal non-quasi-static compression of a gas IS internally reversible.

In an isothermal process $\Delta Q = \Delta W; (\Delta U = 0)$. So if the actual work done in the actual process is equal to the integral of PdV, (ie. the work done in a reversible process), it will be internally reversible: the integral of dQ/T over the actual process will be the same as the integral of dQ/T for the reversible one.

The work done by the gas in the isothermal expansion is less than $\int PdV.$ So it is not internally reversible.

However in an isothermal compression, the work done by the gas (ie. a negative amount of work) is equal to the integral of Pdv over that path. So it is internally reversible.

AM

 

[DrDu]

Andrew, most of your claims only hold true for ideal gasses, not for real gasses. E.g. Delta U is not 0 for isothermal processes and I can think of irreversible isothermal compression of a non-ideal gas. The point is that certain correlation functions of the gas molecules need not be equal to their equilibrium values during the compression.

 

[Andrew Mason]

Andrew, most of your claims only hold true for ideal gasses, not for real gasses. E.g. Delta U is not 0 for isothermal processes and I can think of irreversible isothermal compression of a non-ideal gas.

Yes. I should have made it clear that an isothermal compression of an ideal gas is internally reversible. This is not necessarily the case for a non-ideal gas. And $\Delta U$ need not be 0 for an isothermal compression or expansion of a non-ideal gas.

AM