The second law of Thermodynamics states that the total entropy of an isolated system increases over time, or it remains same in ideal cases (where the system undergoes a reversible process or when it is in a steady state). The first law of Thermodynamics tells the basic definition of internal energy and states the law of conservation of energy. The second law of Thermodynamics deals with the direction of natural process. It states that a natural process is not reversible. For e.g., heat flows from hot to cold region, and never the reverse, unless some external work is done on the system.
In Terms of Entropy
In a reversible process, a very small increase in the entropy (dS) of a system is defined to result from a small heat transfer to a closed system divided by the common temperature (T) of the system and the surroundings that supply of the heat :
dS = \(\frac { dQ }{ T } \) (closed system)
Various Statements of the Planck’s Law :
1. Statement of Kelvin : According to this statement “It is not possible to make an engine in which the working substance can take heat from the source and change it completely into .work and remain unchanged itself in one complete cycle.” It is concluded from this statement that it is not possible to get work continuously from heat source. Actually the sink in necessary and it is necessary to release. Some heat to the sink. This statement is based on the principle of carnot heat engine.
2. Statement of Clausius : According to this statement, “It is an impossible process that in cyclic process the working substance transfers heat from low temperature object to high temperature object directly in the absence of external work.”
It is concluded from this statement that transfer of heat from a low temperature object to a high temperature object on its own is not possible. For this it is important that external work be done on the working substance. This statement is based on the principle of refrigerator.
Equivalence of Clausius and Kelvin Statements :
Let there be an engine violating the Kelvin statement : i.e., one that drains heat and converts it completely into work in a cyclic manner without any other result. Now, pairing it with a reverse Carnot engine.
The newly created engine (consists of two engines) transfers heat ∆Q = Q(\(\frac { 1 }{ \eta } \) – 1) from the colder region (sink) to the hotter region (source), which violates the statement of Clausius. Thus, violation of Kelvin statement means violation of Clausius statement i.e., the Clausius statement implies the Kelvin statement. Similarly, we can prove that the Kelvin Statement implies the Clausius statement and hence both the statements are equivalent.
