Second Law of Thermodynamics

As per the second law of thermodynamics, the total entropy of an isolated system will always increase over time. Entropy is like the measure of randomness or disorder within a system. So, basically, things tend to get messier and more chaotic on their own.

1.0Define Second Law of Thermodynamics 

The second law of thermodynamics is a physical law based on universal empirical observation concerning heat and energy interconversions. The second law of thermodynamics establishes the concept of entropy as a physical property of a thermodynamic system. It predicts whether processes are forbidden despite obeying the requirement of conservation of energy as expressed in the first law of thermodynamics and provides necessary criteria for spontaneous processes. For example, the first law allows the process of a cup falling off a table and breaking on the floor, as well as allowing the reverse process of the cup fragments coming back together and 'jumping' back onto the table, while the second law allows the former and denies the latter.

The second law is concerned with the direction of natural processes. It asserts that a natural process runs only in one sense, and is not reversible. That is, the state of a natural system itself can be reversed, but not without increasing the entropy of the system's surroundings, that is, both the state of the system plus the state of its surroundings cannot be together, fully reversed, without implying the destruction of entropy.

2.0Clausius and Kelvin statements of Second Law of Thermodynamics

Clausius Statement 

The Clausius statement of the second law of thermodynamics focuses on the concept of heat transfer. It states: "Heat cannot spontaneously flow from a colder body to a hotter body."

In other words, if you have two objects at different temperatures, heat energy will naturally flow from the hotter object to the colder one. This statement emphasizes the directionality of heat transfer and is a fundamental principle underlying many natural processes. It's named after Rudolf Clausius, a German physicist who made significant contributions to the study of thermodynamics in the 19th century.

Kelvin statement 

The Kelvin statement of the second law of thermodynamics is another important formulation, and it goes like this:

"No process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work."

In simpler terms, this statement suggests that it's impossible to create a device that extracts heat from a single reservoir and converts all of it into useful work without any other changes occurring. This principle highlights the limitations on the efficiency of heat engines. It's named after Lord Kelvin (William Thomson), a Scottish-Irish physicist who made significant contributions to thermodynamics and other fields in the 19th century.

The violation of the Kelvin statement implies a violation of the Clausius statement, i.e. the Clausius statement implies the Kelvin statement. We can prove in a similar manner that the Kelvin statement implies the Clausius statement, and hence the two are equivalent.

3.0Other Statements of Second Law of Thermodynamics

The second law of thermodynamics can break down into a couple of statements:

1. Entropy Increases: The total entropy of an isolated system will always increase over time. Entropy is a measure of the system's disorder or randomness. This means that, left to its own devices, a system will naturally evolve towards a more chaotic state.

2. Irreversibility: Many natural processes are irreversible. If you break an egg, it's not spontaneously going back together. The second law implies that certain changes in a system are easy to accomplish in one direction (like breaking an egg) but nearly impossible to undo.

3. Heat Flows from Hot to Cold: Heat energy tends to flow from regions of higher temperature to regions of lower temperature. This is the reason your coffee cools down in a room–it's the natural tendency for heat to disperse.

4. Efficiency Limits: The second law of thermodynamics places limits on the efficiency of thermal machines, like engines. No engine can be 100% efficient; some energy is always lost as waste heat.

These statements capture the essence of the second law and its various implications in the behavior of physical systems.

4.0Reversible And Irreversible Process

Reversible Process 

A reversible process is defined as a process that can be reversed without leaving any trace on the surroundings. Both the system and the surroundings are returned to their initial states at the end of the reverse process. 

Conditions for a Reversible process

1. The process should take place very slowly, i.e. quasi-statically, i.e. seemingly static (from the Latin word qasi meaning ‘as if’) so that it satisfies the following requirements at each stage of the process. 
2.  The system should be in mechanical equilibrium.
3.  The system should be in thermal equilibrium.
4.  The system should be in chemical equilibrium, i.e., no new products should be formed. (b) There should be no friction losses etc. It should be remembered that a complete reversible process or cycle of operations is only an ideal case. In actual practice, there is always a loss of heat due to friction, conduction and radiation. However, it is possible to approximate reversible processes through carefully controlled procedures, but they can never be achieved.

Examples

• Frictionless pendulum. 
• Quasi-equilibrium expansion and compression of a gas.

Irreversible Process 

A process that is not reversible is called an irreversible process. The spontaneous processes occuring in nature are irreversible. In fact irreversibility is a rule rather than an exception in nature. 

Examples

1. Sudden unbalanced expansion of a gas. 
2. Heat produced by friction. 
3. Heat generated when a current flows through an electric resistance in any direction.
4. Cooking gas leaking from a cylinder. 
5. Diffusion of liquids or gases. 
6. Breaking of an egg. 
7. The growth of a plant.

A system can be restored to its initial state following a process, regardless of whether the process is reversible or irreversible. But for reversible process, this restoration is made without leaving any net change on the surroundings whereas for irreversible processes, the surroundings usually do some work on the system and therefore will not return to their original state.

5.0Entropy Concept 

To have a better understanding of thermodynamic process and the second law of thermodynamics, let us introduce the concept of entropy. It was introduced by Clausius in 1865.

 A quantity that denotes the amount of disorder is called entropy and is denoted by S. The total energy always conserved in any process but the total entropy always increases or remains the same in any process (ie., the disorder increases or remains constant).

                                                     dS = dQ/T     or          S = ∫dQ/T

This equation is based on the concept that entropy increases with the amount of heat added to a system and decreases with the temperature. The integral sign indicates that this equation is often used for processes where temperature or heat transfer is not constant throughout the process.

For reversible processes, ΔS = 0. For an irreversible process ΔS > 0 A process where ΔS < 0 is not possible.

6.0Heat Engine 

The second law of thermodynamics is fundamental in understanding the operation and limitations of heat engines. In the context of heat engines, the second law imposes constraints on their efficiency and operation:

1. Entropy Production: During the operation of a heat engine, entropy is continuously being produced. This is because heat is transferred from a hot reservoir to a cold reservoir, and this transfer is irreversible. The increase in entropy occurs due to the spreading out of energy and the loss of useful work potential.

2. Limitation on Efficiency: The second law also implies that no heat engine can be 100% efficient. This is known as the Kelvin-Planck statement of the second law. It states that it is impossible to construct a heat engine that, operating in a cycle, produces no effect other than the extraction of heat from a single thermal reservoir and the performance of an equivalent amount of work. In other words, some energy is always lost as waste heat during the energy conversion process.

3. Carnot Efficiency: The Carnot efficiency represents the maximum efficiency that any heat engine can theoretically achieve, and it depends only on the temperatures of the heat reservoirs between which the engine operates. The efficiency of a real heat engine is always less than the Carnot efficiency due to practical limitations such as friction, heat loss, and irreversibilities within the system.

Overall, the second law of thermodynamics provides a theoretical framework for understanding why heat engines have inherent limitations in terms of efficiency and why perfect efficiency is unattainable in practice.

7.0Refrigerator

The operation of a refrigerator also ties closely to the second law of thermodynamics. Unlike a heat engine, which converts thermal energy into mechanical work, a refrigerator transfers thermal energy from a cold reservoir (the inside of the refrigerator) to a hot reservoir (the surroundings) using mechanical work.

Here's how the second law of thermodynamics applies to refrigerators:

1. Entropy Increase: Similar to a heat engine, a refrigerator operation involves an increase in entropy. Heat naturally flows from a warmer object to a cooler one, but a refrigerator reverses this process by using work input to transfer heat from a colder region (inside the refrigerator) to a warmer region (outside the refrigerator or room). This transfer of heat is accompanied by an increase in entropy, contributing to the overall increase in entropy consistent with the second law.

2. Coefficient of Performance (COP): The efficiency of a refrigerator is quantified by its Coefficient of Performance (COP). The COP of a refrigerator is defined as the ratio of the heat removed from the cold reservoir (inside the refrigerator) to the work input required to achieve this heat transfer. Similar to the efficiency of a heat engine, the COP of a refrigerator is limited by the second law of thermodynamics.

3. Reversed Carnot Cycle: The ideal refrigeration cycle, known as the reversed Carnot cycle, provides insight into the theoretical maximum efficiency of a refrigerator. This cycle operates in a similar manner to the Carnot cycle for a heat engine but in reverse. The COP of an ideal refrigerator operating on a reversed Carnot cycle is determined by the temperatures of the cold and hot reservoirs.

Overall, the second law of thermodynamics plays a crucial role in understanding the limitations and efficiency of refrigerators, just as it does for heat engines. It highlights the fundamental principles governing the direction of heat transfer and the constraints on energy conversion processes.

Also Read: First Law of Thermodynamics