# Entropy: second law for systems with zero input net energy

• haushofer

#### haushofer

Dear all,

I'm trying to think about applying the second law of thermodynamics to a system which is not isolated, but has an energy flowing inwards and an equal (!) energy flowing outwards, such that the total energy does not change (total energy flux is zero). Can we still apply the second law in this case? And where can I find a reference (here or elsewhere) which treats this case?

If you compress an ideal gas isothermally, there is an influx of work and equal outflux of heat and the internal energy of the gas doesn't change. ( http://hyperphysics.phy-astr.gsu.edu/hbase/therm/entropgas.html )

Of course if a closed system is in thermal equilibrium with its surroundings, it's constantly exchanging molecular kinetic energy (heat) with the surroundings, but there is no net flow of heat to either direction.

haushofer
Ah, yes, of course, that's a familiar example. Thanks! My thermodynamics is a bit rusty, but I'm reviewing some for applications to cosmology (gravitating systems).

I'm trying to think about applying the second law of thermodynamics to a system which is not isolated, but has an energy flowing inwards

Yes. Here is a place to start.

haushofer
Do we mean the same thing with terms "isolated", "closed", and "open"? An isolated system doesn't exchange either energy or matter with its surroundings. A closed system can exchange heat but not matter. An open system can exchange both heat and matter with the rest of the universe.

Chestermiller
Yes. So I'm referring to the second law for closed systems instead of isolated ones.