# Are "isentropic" and "adiabatic" same?

## Main Question or Discussion Point

Isentropic means a process where entropy remains constant. Now formula for entropy is
ΔS = ΔQ/T
now in an isentropic process, ΔS=0......so that means ΔQ = 0 ....right???
but if ΔQ = 0, that is an adiabatic process.
so are isentropic and adiabatic processes are same thing??
thanks.

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Bystander
Homework Helper
Gold Member
No. Consider a free expansion of an ideal gas into a vacuum between V1 and V2, and compare it to a reversible adiabatic expansion between the same volumes.

Chestermiller
Mentor
Isentropic means a process where entropy remains constant. Now formula for entropy is
ΔS = ΔQ/T
now in an isentropic process, ΔS=0......so that means ΔQ = 0 ....right???
but if ΔQ = 0, that is an adiabatic process.
so are isentropic and adiabatic processes are same thing??
thanks.
Your equation for ΔS is correct only for a reversible path between the initial and final equilibrium states. It is incorrect for a process path that is not reversible.

Chet

So for reversible process, "adiabatic" and "isentropic" are same thing. Right?

Ken G
Gold Member
Right, if you are careful about what you are applying those terms to. Since "adiabatic" means that there is no heat transfer anywhere between the various subsystems, "isentropic" must be used to mean that the entropy of none of the subsystems changes in this reversible process. In any reversible process, the whole universe is isentropic, but the subsystems are also isentropic only if the process is adiabatic.

Chestermiller
Mentor
So for reversible process, "adiabatic" and "isentropic" are same thing. Right?
Yes.

Q_Goest
Homework Helper
Gold Member
Adiabatic means there is no heat transfer into or out of the system. Isentropic means the process is reversible, but it might help to talk about examples of those processes.

Flow of gas through a pipe is restricted by shear forces against the walls, so pressure gradually decreases. This flow can be adiabatic if there is no heat transfer, but because the flow is not reversible (it does no work and we can't recover the original pressure and velocity of the gas further down the pipe) it isn't isentropic.

If we somehow (magically) eliminated frictional losses of a gas through the pipe and eliminated any heat transfer, the pressure and velocity would remain constant and would obey Bernoulli's equation. In this case, we could increase the pipe diameter so that velocity decreased. Further down the pipe we could reduce the diameter back to the original diameter and recover the gas velocity and static pressure per Bernoulli's. In this case, the gas flow is both adiabatic and isentropic. Something simlar to this is important in determining flow though a nozzle for example.

One of the most common processes that is modeled as isentropic is that of gas (or liquid) compression. Gas in a cylinder compressed by a piston has had work done to it. If there is no heat exchange with the environment, and assuming this is reversible (ie: no frictional flow losses), the gas could expand again and come back to it's original pressure and temperature which would be an isentropic process.

It's useful to look at how processes deviate from true adiabatic or isentropic to understand what other things are going on in a given process such as heat transfer or irreversible pressure losses due to flow restrictions.

Note that isentropic processes are always adiabatic but adiabatic processes aren't always isentropic.

Chestermiller
Mentor
Adiabatic means there is no heat transfer into or out of the system. Isentropic means the process is reversible, ...
This statement needs to be qualified. If a process is reversible, it does not necessarily mean that the change in entropy of the system is zero. In order for that to happen, the process must also be adiabatic. The above statement can be corrected if the word "also" is inserted before the word "reversible."
One of the most common processes that is modeled as isentropic is that of gas (or liquid) compression. Gas in a cylinder compressed by a piston has had work done to it. If there is no heat exchange with the environment, and assuming this is reversible (ie: no frictional flow losses), the gas could expand again and come back to it's original pressure and temperature which would be an isentropic process.
In addition to the absence of frictional losses, the expansion must be carried out quasistatically. If it is not done quasistatically, the entropy will increase.

Chet

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