WHAT IS THE SECOND LAW OF THERMODYNAMICS ?

First law of thermodynamics only taught us about the temporal nature of world by which we can only transfer energy or thermodynamic coordinates in each other at the rate of mechanical equivalent of heat also known as joule's equivalent which is defined as -

" we have to do 4.18 J of work to produce 1 calorie of heat "

But second law of thermodynamics give us proper understanding at which term and condition are employed by nature for transformation of thermodynamic coordinate's into primary interest for understanding of how transformation will occur between heat and work .

i want to emphasize one more point about this law, isn't a absolute law about which we will discuss in microscopic level of second law .

considerably there are four scientist's worked on second law , Rudolf Clausius , lord kelvin, max Planck & Ludwig Boltzmann , first three of them worked on classical thermodynamics also known as macro static level thermodynamic & last one worked on microscopic level of thermodynamic where actual meaning of second law lies .

Second law's foundation led by Carnot Principle which states that -

" Efficiency of heat engine depends on the two temperature between which heat engine is working and it's independent of working substance . "

second law could be expressed in many ways but dominated statement's are given by Rudolf Clausius and Lord kelvin & Max Planck .

Rudolf Clausius statement - it is impossible to construct a device which , operating in a cycle , will produce no effect other than the transfer of heat from a cooler body to hotter body

kelvin-planck statement - it is impossible for a heat engine to produce net work while working in a cycle by exchanging heat from only one thermal reservoir

One more argument is very famous about this two statement which is equivalence between them hence when we try to violate one statement other one violates simultaneously than we came on abstract both of them are logically equal statement lets see how we reached on this conclusion

First we will violate Clausius statement -

make a device which takes heat in from lower temperature reservoir and throw out it to higher thermal reservoir without expense of any external work

make a heat engine cycle according to kelvin-planck's statement connected through same reservoir

now here clearly we can see "R" is taking heat "Q" from low temperature thermal reservoir and ejecting same amount of heat to higher temperature

thermal reservoir without expense of any external work ,

and a normal Heat Engine taking heat "Q" from higher temperature thermal reservoir and producing "W" amount of work by ejecting "W-Q" amount of heat to lower temperature thermal reservoir while working in cycle .

here we encounter a fact our Refrigerator is ejecting Q amount of heat to the ThR and our heat engine taking "Q" amount of heat from ThR so, instead of interchanging heat from ThR we can join HE to each other than our system's arrangement will look something like

So this is clear that this device is working in cycle by interchanging heat through only one thermal reservoir which is violation of kelvin-planck's statement .

now come on kelvin planck's statement 's violation here we use alternative approach we will violate kelvin-planck's statement and clausius's statement will violate simultaneously

make a heat engine which is working in a cycle and producing net work while interchanging heat from only one thermal reservoir .

now in system we will add an system according to clausius statement

now care fully observe the diagram , HE is producing work by inter changing heat Q from high thermal reservoir while working in cycle and system "R" is taking heat from TLR and ejecting it to the ThR by consuming some amount of work so ,

here we will join HE output W to input of "R"

Now we can consider "R" & HE as a single device , here "R" is taking W amount of work from HE and Q' amount of heat from TLR and ejecting W+Q' to the sink ;but we know W=Q so total ejection by "R" will be Q+Q' .

But Q is the same amount of heat "R" is taking from THR so instead of interchanging it by reservoir we can give Q amount of heat directly from the HE considering it as a part of individual system

Clearly system is not consuming any work to transfer heat from low thermal reservoir to high thermal reservoir as a refrigerator .

rotation of W=Q is just happening within the system  "R"is not consuming it .

Logic behind both of these statement are energy can not be used 100% in cyclic processes

TH R = Higher temperature thermal reservoir ;

TLR = Lower temperature thermal reservoir ;

"R" = Refrigerator

HE = Heat Engine