Clausius Statement of 2nd Law

The Clausius statement of 2nd law provides for the workings of a refrigerator in a cyclic process in a mechanical system. The first law of thermodynamics has certain shortcomings; for instance, the first law does not explain why some mechanical processes in a closed system are reversed and only occur in one direction. The second law of thermodynamics explains and addresses the limitations of the first law. In this regard, the Clausius statement of 2nd law explains the concept of work done and the efficiency of a refrigerator. The following article gives detailed notes of Clausius statement of 2nd law.

The First Law of Thermodynamics

The first law of thermodynamics is defined for a system that undergoes mechanical approach. The first law states that the energy produced in a system after undergoing a cycle of processes is converted to heat; therefore, no amount of heat is wasted during a mechanical activity. The first law of thermodynamics proves and satisfies the law of energy conservation applications.

The law of energy conservation gives:- “Energy may be transformed from one form to another but the total energy of an isolated system remains constant. Energy can neither be created nor destroyed.”

The Second Law of Thermodynamics

The second law of thermodynamics addresses the shortcomings and limitations of the first law. The second law deals with the efficiency and work done of heat engines; it also limits the coefficient of a mechanical refrigerator. In other words, the second law of thermodynamics for a heat engine working in a cyclic process states that the total efficiency of a heat engine can not be unity.

Therefore, the law implies that heat released to the cold reservoir by the heat engine is never equal to zero. And in a mechanical refrigerator, the second law of thermodynamics gives that the coefficient of performance of the refrigerator is never equal to infinite. Therefore, the second law of thermodynamics implies that the total external work (W ) done on the refrigerator is not equal to zero.

Clausius Statement of 2nd Law

Like the Kelvin and Planck statements, the Clausius statement of 2nd law denies the possibility of a perfect refrigerator.

Clausius’ Statement of 2nd law gives:- “No process is possible whose sole result is the transfer of heat from a colder object to a hotter object.”

In other words, the Clausius statement of 2nd law gives, no such system is possible that can transfer heat from a cooler heat source to a higher temperature heat source; for such a transfer of heat, an additional external source of energy is required. 

The Clausius statement of 2nd law also proves that the process of heat transfer in a system is irreversible and only occurs in one direction. The heat transfers from higher to lower temperature by itself; however, an additional energy source is required to transfer heat from a lower to a higher temperature. 

Refrigerators 

A refrigerator is a system that is defined as a reverse system of a heat engine. Here the working substance or the fuel to the system acquires heat Q2 from the cold reservoir or heat source at a temperature T2. Consider some external work W is done on the system, and an amount of heat Q1 is released to the hot reservoir at temperature T1. We know Q2 is the amount of heat acquired from the cold heat source, 

Let W be the work done on the system of the refrigerant. From the law of energy conservation, the heat released to the hot heat source is given by,

Q1 = W + Q2

 α = Q2 / (Q1 – Q2) 

Where, 

α = the coefficient of performance of the refrigerator

α = Q2 / W

A refrigerator system can not perform work by itself; it will require an additional energy source. Likewise, a heat engine system can not convert the total heat into the total work done. Therefore, the coefficient of performance (α) in the above expression cannot be infinite.

Coefficient of performance

The working substance in a refrigerator is generally a gas. In a cyclic process, the working substance goes through the following steps: 

1. The gas acting as the working substance of the system suddenly expands and converts into a mixture of vapour and liquid.

2. The cool liquids observe heat, and vapour is formed. 

3. The external energy source works on the system, and the vapour is heated up.

4. Heat is released in the form of vapour in the surroundings.

5. The process is repeated.

The coefficient of performance of a system of the refrigerator is given by the following:-

α = Q2 / W.

Practical Usage of Clausius’s Statement

The major applications of Clausius’s statement of 2nd law are seen in cooling devices. Appliances like coolers, refrigerators, and air-conditioners are all based on Clausius’s statement of 2nd law of thermodynamics.

Conclusion

A refrigerator is defined as a closed mechanical system that works in a cyclic process and transfers heat from a lower temperature heat source to a higher temperature heat source. The Clausius statement of 2nd law derives a statement for the work done on the refrigerator; this statement has a wide range of applications in our day-to-day life. The concept is for the working of various cooling appliances incorporated with refrigeration; some examples include coolers, air conditioners, and fridges. The above article looks into the Clausius statement of 2nd law importance of thermodynamics and its practicality.