# How is change in entropy of universe related to the energy released by system that can be used to do work?

What does change in entropy ($\Delta S$) represent ? How does change in entropy of a universe ($\Delta S_{univ}$) give us information about energy available to do work.

I would like to know the physical significance of entropy of universe and how it is related to energy energy released by system that can be used to do work (Not in terms of equation. I would want to know its physical significance).

## 2 Answers

Well a reaction which is spontaneous has negative value of Gibbs or Helmholtz free energy. This free energy is the energy which is made available to be used for work.

How does that relate to your question? Both Gibbs and Helmholtz free energy are derived from the argument that change in entropy of the universe is greater than zero. Physically, that is an argument that no chemical system will react in such a way that decreases the number of available microstates unless it increases the number of available microstates for the surroundings by a greater amount.

Suppose you are a magician & want to make a rabbit having internal energy $U$. so, in order to invoke the rabbit, you have to supply $U$. But wait! In order to make the rabbit, you not only have to provide $U$ but also the energy necessary to create space for the rabbit by asiding the atmosphere. So, the total energy you supply is $U + PV$. This is enthalpy. But again wait! You don't have to supply the entire $U + PV$ as there is an associated entropy with the formation of the rabbit i.e. $S$ i.e. the energy supplied by you, the Great Magician is $U + PV - T S$. This is the free energy as it is the only energy you will get after vanishing the rabbit.

• This analogy was mentioned by Daniel V. Schroeder. – user5764 Jul 19 '15 at 9:06