# I Adiabatic process in statistical mechanics

#### orisomech

Why is a thermally isolated process that occurs sufficiently slow is necessarily adiabatic and not just reversible process ? Here I mean that the definition of adiabatic process is no change in the entropy of the subsystem, and a reversible process is define by no change of the total entropy of all the system . For example, gas in a box that its volume is changing slowly- the entropy of the gas is the box is constant if there is no heat flow.

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#### jambaugh

Gold Member
In part the word "sufficiently" in "sufficiently slow[ly]" is defining the process as adiabatic, but the key point is, I believe, that for sufficiently slow processes the system is at maximal entropy at all times.

If you add thermal isolation (and mass isolation) then the presumption is that the entropy cannot change. What can change is total energy in the form of work done on the system. But since the system is thermally and substantively isolated the fact that the process is reversible with only zero entropy energy exchange in the form of work being done to or by the system, we must assume no entropy change.

#### MisterX

Here I mean that the definition of adiabatic process is no change in the entropy of the subsystem, and a reversible process is define by no change of the total entropy of all the system .
Hello, perhaps there is some confusion about these terms. Adiabatic means no heat is transferred to or from the subsystem and its surroundings. It does not say anything about the entropy change. The word for no entropy change is isentropic or reversible. A slowly carried out adiabatic expansion under pressure from a friction-less piston is approximately a reversible process (0 entropy change). However there are other forms of (approximately) adiabatic expansion that are not reversible. One of the notable ones is free expansion into a vacuum. Free expansion will tend to increase the entropy. Another irreversible adiabatic process is a gas/fluid escaping through a small opening which is called Joule-Thompson expansion or throttling. Joule-Thompson expansion has approximately constant enthalpy (isenthalpic).

Some of these processes may be approximately adiabatic because they happen fast - no long enough for significant amount of heat to be transferred to the container.

There are also processes which are reversible but not adiabatic, like reversible isothermal expansion.

Well, thermodynamics can be a difficult subject but I think this is accurate to my understanding.

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#### orisomech

Since in the book of Landau and Lifshitz they have different definitions, let me rephrase my question that I meant to ask:
Gas in a box that its volume is changing slowly enough- the entropy of the gas is the box is constant if there is no heat flow. What I ask is why is the entropy of the gas in the box is constant, and not just the total entropy of the box and the environment together.

#### Chestermiller

Mentor
Are we allowed to use classical thermodynamics to explain this, or does it have to be explained using statistical thermodynamics?

#### orisomech

Are we allowed to use classical thermodynamics to explain this, or does it have to be explained using statistical thermodynamics?
I prefer statistical thermodynamics

#### DrDu

The point is that "adiabatic" has slightly different meanings in different fields: On a greek airport, it means "no passage". In phenomenological thermodynamics, specifically, it means no passage of heat.
But it is also used in quantum mechanics. There, an adiabatic change means a time dependent change of a hamiltonian $H(t)$ such, that if the system is initially in an eigenstate of $H(0)$, it will be in the corresponding eigenstate of $H(t)$ at time t. Hence there is no passage between eigenstates. If the system is initially in a mixed state with density matrix P, the entropy of this density matrix will not change. So for an adiabatic quantum mechanical process, there will be no change of entropy. Therefore in statistical mechanics, you have to look out in which sense "adiabatic" is used anytime.

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