## Third Law of Thermodynamics – 3rd Law

*The entropy of a system approaches a constant value as the temperature approaches absolute zero.*

Based on empirical evidence, this law states that the **entropy of a pure crystalline substance is zero** at the **absolute zero of temperature**, 0 K and that it is impossible by means of any process, no matter how idealized, to reduce the temperature of a system to absolute zero in a finite number of steps. This allows us to define a zero point for the thermal energy of a body.

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The third law of thermodynamics was developed by the German chemist **Walther Nernst** during the years 1906–12. For this research Walther Nernst won the 1920 Nobel Prize in chemistry. Therefore the third law of thermodynamics is often referred to as **Nernst’s theorem** or **Nernst’s postulate**. As can be seen, the third law of thermodynamics states that the entropy of a system in thermodynamic equilibrium **approaches zero** as the **temperature approaches zero.** Or conversely the **absolute temperature **of any **pure crystalline substance** in thermodynamic equilibrium **approaches zero** when the **entropy approaches zero.**

**Nernst Heat Theorem** (a consequence of the Third Law) is:

*It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations.*

Mathematically:

The **Nernst heat theorem** was later used by a German physicist Max Planck to define the third law of thermodynamics in terms of entropy and absolute zero.

Some materials (e.g. any amorphous solid) do not have a well-defined order at absolute zero. In these materials (e.g. glass) some finite entropy remains also at absolute zero, because the system’s microscopic structure (atom by atom) can be arranged in a different ways (W ≠ 1). This constant entropy is known as the residual entropy, which is the difference between a non-equilibrium state and crystal state of a substance close to absolute zero.

Note that the exact definition of entropy is:

**Entropy = (Boltzmann’s constant k) x logarithm of number of possible states**

*S = k*_{B}* logW*

This equation, which relates the microscopic details, or microstates, of the system (via *W*) to its macroscopic state (via the **entropy S**), is the key idea of statistical mechanics.

## Absolute Zero

**Absolute zero** is the coldest theoretical temperature, at which the thermal motion of atoms and molecules reaches its minimum. This is a state at which the enthalpy and entropy of a cooled ideal gas reaches its minimum value, taken as 0.

Mathematically:

*lim S _{T→0} = 0 *

*where*

*S = entropy (J/K)*

*T = absolute temperature (K)*

**Classically**, this would be a state of **motionlessness**, but **quantum** uncertainty dictates that the particles still possess a **finite zero-point energy**. **Absolute zero** is denoted as 0 K on the Kelvin scale, **−273.15 °C** on the Celsius scale, and **−459.67 °F** on the Fahrenheit scale.

## Relation to Heat Engines

According to the **Carnot’s principle,** that specifies limits on the maximum efficiency any heat engine can have is the Carnot efficiency.This principle also states that the efficiency of a Carnot cycle depends solely on the difference between the hot and cold temperature reservoirs.

where:

- is the efficiency of Carnot cycle, i.e. it is the ratio
**= W/Q**of the work done by the engine to the heat energy entering the system from the hot reservoir._{H} - T
_{C}is the absolute temperature (Kelvins) of the cold reservoir, - T
_{H}is the absolute temperature (Kelvins) of the hot reservoir,

The third law dictates that T_{C} can never be zero, therefore we see that a 100% efficient heat engine is not possible.

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