A hot object in thermal contact with a cold one will finally reach a temperature in between. Why can the entropy change of each object be calculated as if the process was reversible? Is there a reversible process with the same final and initial state and what would that be?
Entropy is a thermodynamic property. So, the difference between the entropy of two known states does not depend on the process. The second question: Yes, provided there is an adequate heat exchange.
Yes, that's exactly my point. The text book by Young and Freedman simply calculates the change of entropy as if heat conduction was reversible without even trying to construct a reversible process with the same initial and final state. The explanation given is: "Although the processes are irreversible we calculate entropy changes as if they were reversible." Not very satisfying! Is there a straight forward, equivalent reversible process that this book fails to mention?
Yes. But such a process must present a heat exchange in order to satisfy the Clausius inequality
The Clausius theorem is only valid for cyclic processes if I'm not mistaken. Are you saying that one should think of a cyclic process that uses the hot and the cold object as heat source and sink and keeps running until the temperatures are the same?
No! Please consider the Clausius-Duhem [Slattery - McGraw-Hill] inequality for a single process. In fact I am working under a Continuum Mechanics viewpoint.
Okay, this is way above the level of a course for first year physics students. I was hoping for a much simpler explanation. Thank you anyway.
Entropy is a state function. That is, it is dependent only on the current equilibrium state of the system. That means entropy changes do not depend on the path taken from one state to another. In mathematical terms, you might think of differential entropy changes as exact differentials. You can find lots of examples of simple mathematical functions that depend upon the integration path, and other simple functions that depend only on the initial and final states. In short, then, you don't have to come up with or imagine any reversible process that arrives at the same final state as an irreversible process - it is enough to know that entropy changes are independent of the path...the initial and final equilibrium states are all that matter.
I will attempt to give a simpler (if more trivial) explanation! It strikes me that with the given information, only the "reversible entropy change" can be calculated. The information in the problem is insufficient to find the "irreversible entropy change" which must be larger.
Entropy change of hot object and entropy change of cold object can be found separately depending on their initial state and final equilibrium state.(use state equation to find entropy change)For hot body it becomes - ve and for cold body it is +ve.More over entropy is a state function and hence does not depend on process .Of course whether the process is reversible or irreversible the value will not change.But for the Universe it is +ve if you treat it as spontaneous/Natural or irreversible exchange.Universe entropy change is zero if you assume that the exchange of heat is reversible.The final equilibrium temperature and state will differ basing on your assumption whether it is reversible or irreversible.
For your second question if the states are same by definition you cant say a process has happened.Hence such thing does not exist.If process occurred and it has returned to initial state it is called a cyclic process(May be reversible or irreversible) for which entropy change is zero and there are many examples for cyclic process.
As was pointed out several times already, entropy is a state function, and therefore only depends on the initial and final state of the system. If you know the functional dependence of S on your control parameters (temperature, pressure, electric field ...) you can calculate the entropy change for any process, since it does not depend on the path (that is what state function also implies).
However, if you want to measure the change in entropy between two states, you need to find a reversible path between them and evaluate \intif dqrev/T . Using an irreversible process connecting the two will give a value for ∆S that is too low.
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
- Badges
- Science topic
- Similar topics
- Engineering
- Thermal Engineering
- Thermofluid
- Heat Transfer