# Heat Entropy

A brief introduction to heat entropy and isentropic processes

### Key Facts

**Gyroscopic Couple**: The rate of change of angular momentum () = (In the limit).

- = Moment of Inertia.
- = Angular velocity
- = Angular velocity of precession.

## Overview

**Key facts**The change in entropy for a system undergoing a reversible process is given by: where is the temperature of the system, and the infinitely small amount of heat which is absorbed by the system in a reversible way. Isentropic processes are processes which are assumed to proceed without changes in the entropy of the system. It can be shown that any reversible adiabatic process is an isentropic process.

In order to define the heat entropy, consider the curve of state diagramed in Figure 1.
This curve of state is plotted on a graph with the absolute temperature on the ordinate, such that the area under the curve represents the heat supplied or rejected. The quantity along the abscissa is a property, or function of state, called entropy, and denoted by the letter .
As entropy is a function of state, changes in its value depend only on the initial and final state, and not on the process which causes the change. The change in entropy for a system undergoing a reversible process (for a more detailed discussion on reversible processes also see Reversible Processes ) can be written as:
where is the temperature of the system, and the infinitely small amount of heat which is absorbed by the system in a reversible way.