Third Law in Thermodynamics

The third law of thermodynamics states that the entropy of a pure substance in a perfect crystalline state at zero temperature is zero. The third law of thermodynamics defines that the temperature of a system proceeds towards absolute zero, but its entropy becomes constant, or the change in entropy is zero. The third law of thermodynamics forecasts the behavior of entropy and the properties of a system in a unique environment, known as absolute temperature. This law assists in computing the absolute entropy of a substance at any given temperature. This resoluteness is traditionally based on heat capacity measurements.

Absolute Zero

According to the law of thermodynamics, when the entropy of a perfect crystal comes to zero, then this phenomenon is called absolute zero. It means a temperature at which a thermodynamic system has the lowest energy. It corresponds to −273.15 °C on the Celsius scale and −459.67 °F on the Fahrenheit scale. At −273.15 °C on the Celsius scale, the particles stop moving, and all disorganization disappears so that nothing can be colder than absolute zero on the Kelvin scale. The entropy of any pure crystalline substance at absolute zero temperature is equal to zero. The temperature scale with zero for its zero point is an absolute temperature scale or a thermodynamic scale. The notion of absolute zero as a limiting temperature has many thermodynamic consequences.

Entropy

The concept of entropy was first introduced in 1850 by a German Physicist named Rudolf Clausius. The measure of a system’s thermal energies per unit of temperatures inaccessible for practical work is known as entropy. Entropy refers to a scientific concept and a measurable physical property commonly related to a state of disorder, randomness, and unpredictability. The entropy concept enables deep insights into the voluntary change direction for varied common phenomena. 

The entropy idea usually provides a mathematical  way for encoding the intuitive concept of impossible processes, even though they would not contravene the fundamental law to conserve energy. This concept was derived from deducing a measurable quantitative direction of spontaneous change. Some of the factors that judge a substance’s entropy is its temperature. It is directly proportional to the temperature of the body. The deduced equation can determine absolute entropy as  

ΔS = QT, where each of the terms is described below:

T is the Temperature, ΔS is the difference in the system entropy, and Q is the absorbed heat.

Third law Mathematical explanation

As per statistical mechanics, the entropy of a system can be demonstrated via the following equation:

S – S0 = 𝑘B ln𝛀

Where,

• S =the entropy of the system.

• S0 denotes the initial entropy.

• 𝑘B designates the Boltzmann constant.

• 𝛀 refers to the total number of microstates compatible with the system’s macroscopic configuration.

 An example of a perfect crystal with exactly one unique ground refers to 𝛀 = 1. Therefore, the equation is rewritten as follows:

S – S0 = 𝑘B ln(1) = 0 [because ln(1) = 0]

When the primary entropy of the system is selected as zero, the following value of ‘S’ can be obtained:

S – 0 = 0 ⇒ S = 0

Therefore, the entropy of a perfect crystal at absolute zero equals zero.

Application of the Third Law of Thermodynamics

Applying the third law of thermodynamics helps calculate the absolute entropy at any temperature ‘T’ These calculations are based on the heat capacity measurements of the substance. 

There are two major applications of the third law of thermodynamics, which are given below.

   1. The third law of thermodynamics is used. It helps to find if substances are pure crystalline or not?

    2. It helps find the absolute entropy related to substances at a specific temperature.

The third law of thermodynamics refers to perfectly crystalline substances to find whether the substance is pure crystalline or not. It defines the entropy of a perfectly Crystalline substance that might be zero at Kelvin temperature. If the substance is not perfectly crystalline, its entropy will not be zero at 0 Kelvin temperature.

Such substances will not be purely crystalline substances. The substances will be imperfect within their crystal structure and show some disorders. Thus, whether the substances are purely crystalline or not could be found.

To find the absolute entropies of substances at a given temperature, utilizing the third law of thermodynamics. The comparison over entropies of a given substance at T temperature with the entropy of that substance at zero Kelvin temperature. We should estimate the changes within entropies between the temperatures.

Contradiction with the other laws of Thermodynamics

The third law of thermodynamics defines absolute zero as a state, whereas the second Law of Thermodynamics denotes that the temperature can never become zero. Based on the second law, the heat cannot spontaneously be moved from a colder body to a hotter body. If a system tries to reach absolute zero, its actual tendency is to draw heat from an external environment, and if it happens. As a result, it will never reach absolute zero. 

On the other hand, the first law defines that energy can neither be created nor be destroyed. In that case, the heat energy has to be drawn from outside the system, which ends the chances of the system reaching absolute zero. 

Conclusion 

In the above content, we have discussed the importance of absolute zero and entropy and how these two aspects make up the third law of thermodynamics. This law states that absolute zero temperature is not possible in physics. This is often overlooked whenever anybody tries to attain zero temperature and regains temperature from the external environment and other sources. Hence, this law is highly intuitive to real-life applications.