## Specific Entropy

The entropy can be made into an **intensive**, or **specific**, variable by dividing by the mass. Engineers use the specific entropy in thermodynamic analysis more than the entropy itself. The specific entropy (s) of a substance is its entropy per unit mass. It equals to the total entropy (S) divided by the total mass (m).

s = S/m

where:

s = specific entropy (J/kg)

S = entropy (J)

m = mass (kg)

Entropy quantifies the energy of a substance that is no longer available to perform useful work. Because entropy tells so much about the usefulness of an amount of heat transferred in performing work, the steam tables include values of **specific entropy** (s = S/m) as part of the information tabulated.

In general, specific entropy is a property of a substance, like pressure, temperature, and volume, but it cannot be measured directly. Normally, the entropy of a substance is given with respect to some reference value. For example, the specific entropy of water or steam is given using the reference that the **specific entropy** of water is **zero** at **0.01°C** and **normal atmospheric pressure**, where s = 0.00 kJ/kg. The fact that the absolute value of specific entropy is unknown is not a problem, however, because it is the change in specific entropy (∆s) and not the absolute value that is important in practical problems.

## Temperature-entropy Diagrams – T-s Diagrams

In general, the phases of a substance and the relationships between its properties are most commonly shown on **property diagrams**. A large number of different properties have been defined, and there are some dependencies between properties.

A** Temperature-entropy diagram** (**T-s diagram**) is the type of diagram most frequently used to analyze energy transfer system cycles. It is used in thermodynamics to visualize changes to temperature and specific entropy during a thermodynamic process or cycle.

This is because the **work** done by or on the system and the **heat added** to or **removed** from the system can be visualized on the **T-s diagram**. By the definition of entropy, the **heat** transferred to or from a system equals the **area under the T-s curve** of the process.

**dQ = TdS**

An** isentropic process** is depicted as a **vertical line** on a T-s diagram, whereas an isothermal process is a horizontal line. In an idealized state, compression is a pump, compression in a compressor and expansion in a turbine are isentropic processes. Therefore it is very useful in power engineering, because these devices are used in thermodynamic cycles of power plants.

Note that, the isentropic assumptions are only applicable with ideal cycles. Real thermodynamic cycles have inherent energy losses due to inefficiency of compressors and turbines.