The findings on second law of thermodynamics by Carnot were further bolstered by the research carried out by a number of scientists. Two other statements that became popular came from Kelvin-Planck and Clausius. All these have been described here.
Second Law of Thermodynamics Statement Based on Carnot’s Findings
This is probably the oldest of all the statements, it says, “The natural tendency of the heat is to flow from high temperature reservoir to low temperature reservoir." It was based on the findings of Sadi Carnot in 1824, who said that the efficiency of the heat engine is not dependent on the type of working fluid but on the maximum and minimum temperature within the cycle.
Carnot said that the work produced by the engine is not due to consumption of heat; rather it is due to transportation of heat from high temperature reservoir to the low temperature reservoir. The efficiency of heat engine cycle increase as the value of the maximum temperature within the cycle increases and the value of minimum temperature within the cycle reduces. The more is the difference between the maximum and minimum value more is the efficiency of the heat engine cycle. Carnot cycle gives the maximum efficiency that can be obtained in the heat engine cycle.
Second Law of Thermodynamics Statement by Kelvin-Planck
Kelvin-Planck’s statement is based on the fact that the efficiency of the heat engine cycle is never 100%. This means that in the heat engine cycle some heat is always rejected to the low temperature reservoir. The heat engine cycle always operates between two heat reservoirs and produces work.
The statement made by Kelvin-Planck for third law of thermodynamics says, “It is impossible for a heat engine to produce net work in a complete cycle if it exchanges heat only with bodies at a single fixed temperature." Thus to produce the work the cycle should exchange heat with two reservoirs which are a different temperatures. The high temperature reservoir is called as source and low temperature reservoir is called as sink.
As per the above statement the net work will be produced in the cycle as long as there is difference in temperature between the source and sink. In due course of time if source loses too much heat and sink gains too much heat and their temperatures become equal, the net work produced in the cycle will be zero.
The Kelvin-Planck statement tells the condition for producing work within the cycle, the Carnot’s statement tells maximum work or efficiency that can be obtained within the cycle.
Second Law of Thermodynamics Statement by Clausius
As we know from the previous statement the natural tendency of the heat is to flow from high temperature reservoir to the low temperature reservoir. But what if we have to transfer the heat from low temperature to high temperature reservoir? This has been clarified by Clausius statement of second law of thermodynamics, which says that the reverse transfer of heat never occurs spontaneously.
The statement of second law of thermodynamics made by Clausius goes like this, “It is impossible to construct a device which, operating in a cycle, will produce no effect other than the transfer of heat from a colder to a hotter body." The statement says that to transfer the heat from low temperature to high temperature reservoir some external work should be done on the cycle. This statement has been the basis for the working for all refrigerators, heat pumps and air-conditioners.
Book: Engineering Thermodynamics by P K Nag