Ok, so. The second law says that all systems will tend to a maximum entropy at equilibrium,
In an isolated system, equilibrium is reached at the time the entropy of the system reaches its absolute maximum, yes.
and they MUST be isolated or we can not truly tell what that maximum is.
This is the first time Ive ever heard that the Second Law is dependent on our ability to determine what state the system is in.
There are methods by which we can determine the entropy of a system while a process is ongoing. Think of a solid mass across which there exists a heat gradient maintained by sinks at either end. The system is not isolated, is obviously not at equilibrium, and has a known constant temperature gradient and quasi-static heat flow, which means you know exactly what the entropy is at any local region in the system.
But obviously one cant know how much total entropy will be generated until the process ceases.
However, entropy itself does still apply to open systems, such as the refrigerator, but they will not tend to a maximum cause energy is being input into the system. After all, a fridge is a non-spontaneous system and only works when plugged in.
Heat pumps are not open systems - no mass crosses any of the system boundaries. I think you mean closed, non-isolated systems: no mass can cross the system boundaries, but energy can.
Imagine an isolated system of two masses of water, one a hot vapor and the other a cold block of ice. They are of just the right size so that the heat heat required to fully melt the ice is the exact amount required to fully condense the steam. The two masses are brought into contact just long enough to fully melt the ice and condense the steam in a quasi-static process. The entropy changes are as follows:
The steam has a mass of 1.0 kg, is at the vaporization temperature (373 K)and has intensive entropy of 15.9 kJ/kg*K. The heat flow out of the steam is 2257 kJ, which reduces the ability of the steam to do work (i.e., lowers its entropy). During this process the steam changes phase from a gas to a liquid without changing temperature, and at the end it has an intensive entropy of 9.6 kJ/kg*K. Thus the change in the intensive entropy of the steam is 9.6 - 15.9= -6.3 kJ/kg*K.
The ice has a mass of 6.8 kg, is at the freezing temperature (273 K) and has an intensive entropy of 0.0 kJ/kg*K. The heat flow into the ice is 2257 kJ (the same as the heat that came out of the steam),which increases the ability of the ice to do work (i.e., raises its entropy). During this process the cold mass changes phase from a solid to a liquid without changing temperature, and at the end it has an intensive entropy of 8.3 kJ/kg*K. Thus the change in the intensive entropy of the cold mass is 8.3 0.0= 8.3 kJ/kg*K.
The total entropy generated by this process is given by dS = (-2257/373) + (2257/273) = -6.3 + 8.3 = 2.0 kJ/K.
It is this sum which the Second Law demands must be greater than or equal to zero, and it holds for every processs.
Now look at a system that is identical to the first in every way, except that it is closed, not isolated. Heat from an outside sink at 373K is quasi-statically added to the steam during the process, flows quasi-statically from the steam to the ice, and is rejected quasi-statically from the ice to yet another outside sink at 273K. You can readily see that at any time during the process the macrostates of the steam and the ice do not change, so in that sense the entropy of the system remains constant: there is no change in the number of microstates available to the molecules of the system. And yet heat is flowing through the system in an irreversible process, and the total entropy generated is again 2.0 kJ/K, as required by the Second Law.
Rust forming over time is a spontaneous reaction, and requires no outside energy. There is still a net entropy change. Just not to a maximum.
Perhaps you wish to rephrase that? Given a finite amount of iron and oxygen,
Nevertheless, the true 2nd law, MUST be an isolated system. Shall I send you a scan of my textbook pages lol?
Are you quite sure that thats exactly what your text says?
I have no doubt that your text includes proofs that the entropy of a closed system must increase in an irreversible adiabatic process, or that the entropy of an isolated system must increase in any irreversible process (which is a special case of the first), but does it actually say that the Second Law applies only to isolated systems?
). There's nothing more I need to do than point out this small detail: the Second Law tells us something about thermodynamically isolated systems, but refridgerators aren't thermodynamically isolated systems. If the fridge were an isolated system, then the Second Law would apply, and we could say with certainty that the entropy of the entire system would tend to a maximum. But it's not, so we can't, and indeed we observe that, when powered, entropy decreases.
