I had some doubts regarding the concept of entropy. My first doubt was

  1. Entropy is defined as $ dS = dQ _{rev}/ T $ yet my textbook says that entropy is a state function. Isn't it the definition of a state function that we can define its value uniquely depending on the current system with no regards to the previous states of the system, yet in the formula for entropy we need to find the change in its heat energy which is not uniquely determined by the system and we need the previous state of the system to define it properly.

  2. My course says that entropy is strictly defined only for reversible paths, that is all processes done on the system must be strictly reversible, however there are no such restrictions for that on the surrounding. What is the reason for such a definition of entropy and why we can't define it for irreversible processes on the system? The only reason my course if providing is that because the concept of entropy is derived from the working of a Carnot Engine, where the system has reversible processes done on it, we confine the definition of entropy as such as well.

  3. Another doubt that I had was if we do want to calculate the change in entropy of a system if we provide it $ dQ$ heat reversibly, how do we ensure that the temperature of the system does not change, since for calculation of $ \Delta S$ they only consider the change in heat energy and not that of temperature.

  • 2
    $\begingroup$ If you consider the alternate definition, S = k ln W, it is easier to see that entropy is a state function. $\endgroup$ Nov 28 '21 at 15:10
  • $\begingroup$ For 1, the essence is this: A state function depends on states. However, accessible states could depend on path, so state function appears to be dependent on path. $\endgroup$
    – TheLearner
    Dec 1 '21 at 22:14

To get the change in entropy between equilibrium states of a system, you do not need to know the absolute value of the entropy in either state. All you need to know is the integral of dQ/T for a reversible path between the states. Entropy is a state function even though Q depends on path because the integral of dQ/T is the same for all reversible paths between the same two end states.

Does your book say that entropy is defined only for reversible paths, or does it say that the integral of dQ/T is equal to the entropy change only for a reversible path? I think the latter. Entropy change is defined for an irreversible process between two thermodynamic equilibrium states. But to determine the entropy change of the system for such a process, you need to devise an alternate reversible path for the change, and calculate dQ/T for that reversible path.

The integral of dQ/T includes the changes in T over a reversible path, and does not require that T be constant for the reversible path.


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