## Units of Entropy

The SI **unit for entropy** is **J/K**. According to Clausius, the entropy was defined via the change in entropy S of a system. The change in entropy S, when an amount of heat Q is added to it by a reversible process at constant temperature, is given by:

Here **Q** is the **energy transferred** as heat to or from the system during the process, and T is the temperature of the system in kelvins during the process. If we assume a reversible **isothermal process**, the total entropy change is given by:

**∆S = S _{2} – S_{1} = Q/T**

In this equation the **quotient Q/T** is related to the increase in disorder. Higher temperature means greater randomness of motion. At lower temperatures adding heat Q causes a substantial fractional increase in molecular motion and randomness. On the other hand if the substance is already hot, the same quantity of heat Q adds relatively little to the greater molecular motion.

## Example: Entropy change in melting ice

Calculate the **change in entropy** of 1 kg of ice at 0°C, when melted reversibly to water at 0°C.

Since it is an isothermal process, we can use:

**∆S = S _{2} – S_{1} = Q/T**

therefore the entropy change will be:

∆S = 334 [kJ] / 273.15 [K] =** 1.22 [kJ/K]**

where 334 kilojoules of heat are required to melt 1 kg of ice (latent heat of fusion = 334 kJ/kg) and this heat is transferred to the system at 0°C (273.15 K).

## 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.

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