Two Most Popular Definition of Second Law: Kelvin-Planck’s And Clausius’s Statement

There are two most popular statements of second law of thermodynamics i.e. Kelvin-plank statement and Clausius statement.

KELVIN-PLANKS STATEMENT

It is impossible to make an engine (operating in a cycle) which works on the single temperature source and convert all of its heat completely in to work.

This picture will make you understand Kelvin Planck’s statement very easily. This figure shows that the engine is continuously taking heat from the heat source and converting this heat into equal amount of work.

This phenomenon is possible according to 1st law of thermodynamics as energy is conserved. But it does not obey the Kelvin-plank statement of second law.  

Thus, Kelvin Planck’s statement simply wants to say that – “A heat engine must exchange the heat with at least two thermal reservoirs, one at higher temperature and other at lower temperature, then only the engine will operate”. 

This type of heat engine (as shown in above figure) is possible according to the statement/definition of second law of thermodynamics, because it is operating between two temperature reservoirs one at a higher temperature and other at a lower temperature. 

      

This engine will give efficiency less than 100%. This means that no heat engine have 100% efficiency except the "Carnot Engine" because heat can not be completely converted to work. Heat engine obeys first law (Energy is conserved and transferred from one form to other) as well as second law of thermodynamics (Heat can not be completely converted into work).

CLAUSIUS STATEMENT

It is impossible to construct a device (operating in a cycle) that can transfer heat from cold body to the hot body without absorbing any external work. That means, energy (or heat) can not flow itself/spontaneously from a lower temperature body to a higher temperature body.

This picture will make you understand Clausius statement very easily. As shown above, This heat pump absorbs heat from a lower temperature body and rejects heat to a higher temperature body without supply of any work which violates the Clausius statement of second law. 

         This phenomenon is possible according to 1st law of thermodynamics. But it does not obey the Calusius statement of second law of thermodynamics. Thus, such a device can not transfer heat from lower temperature body to higher temperature body without any supply of work to it.

Thus, Clausius Statement simply wants to say that "A heat pump must exchange the heat from lower temperature reservoir to a higher temperature reserve by consuming some external work". 

Now see this image. This type of heat pump is possible according to the statement/definition of second law of thermodynamics, because it is consuming some work in order to transfer heat from lower temperature body to higher temperature body. Thus, this heat pump obeys 1st law as well as 2nd law of thermodynamics.

HOW KELVIN PLANCK’S AND CLAUSIUS’S STATEMENT ARE RELATED TO EACH OTHER????

As we have seen above both statements of second law of thermodynamics i.e. Kelvin-Planck and Clausius statement and we may think that these two statements are different with each other. But if we will analyze these statements, we will conclude that both statements ,i.e., the Clausius and Kelvin-Planck statements of the second law are entirely equivalent. 

This Equivalence can be demonstrated by showing that the violation of either statement can result in violation of the other one. Let us see the following figure,

Here, Heat Pump is receiving heat energy Q₁ from a cold reservoir and delivering this heat energy Q₁ to a hot reservoir without securing any work energy from surrounding. Hence, we can say that clausius statement of second law of thermodynamic is not followed here by the system and Clausius Statement is violated here. Now, let us see here that whether Kelvin-Planck statement is also violated or not for this system.

     

Let us consider one heat engine which is also operating between the same thermal reservoirs as shown in figure. Hot reservoir has temperature T₁ and Cold reservoir has temperature T₂. Heat engine is receiving heat energy Q₁ from hot reservoir and producing net work W by rejecting heat energy Q₂ to cold reservoir. We have considered here that heat engine is receiving same quantity of heat energy which is discharged by heat pump to a hot reservoir. 

Therefore, hot reservoir could be eliminated here as the discharged quantity of heat energy by the heat pump could be taken as input heat energy by the heat engine. 

Now, we can see here that heat engine and heat pump consisting one heat engine which is producing work 'W' during working together in a cycle by exchanging heat energy from a single reservoir and it shows that this system has not followed the Kelvin-Planck statement of second law of thermodynamics. Or we can say that Kelvin-Planck statement of second law of thermodynamics is also violated here for this system. 

        

Similarly, we can show that if a thermodynamic system is not following the Kelvin-Planck statement of second law of thermodynamics then it will also not follow the Clausius statement too.

!!!!So, We Have Proved Here That Kelvin Planck  Statement And Clausius Statement Of Second Law Of Thermodynamics Are Equivalent With Each Other In Each Respect!!!!

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