All about Second Law of Thermodynamics?

Why second law of thermodynamics introduced? 

We know that some processes occur spontaneously but if we try to reverse the direction of process, the process do not occur spontaneously and further some external energy is required to move the given system away from state of equilibrium. 

The question is that "why such reversed processes do not occur spontaneously?" could not be answered by first law because the total energy of system would remain constant in the reversed process as it did in the orginal path and ther is no voilation of first law. Therfore there must be some other natural principle in addition to first law which determines the direction in which a process can take place in an isolated system. This principle is "second law of thermodynamics" .

Second law infers us that "the entropy of universe tends to maximum". 

Second law of thermodynamics in terms of entropy:

  "The entropy of an isolated system is fully conserved in every reversible process i.e. for every reversible process the sum of all changes in entropy taking place in an isolated system is zero. If the process is not a reversible one, then the sum of all changes in entropy taking place in an isolated system is greater than zero. In general we can say that in every process taking place in an isolated system the entropy of system either increases or remains constant."  

Condition for equilibrium of an isolated system

“If an isolated system is in such a state that its entropy is maximum, any change from that state would evidently lead to decrease in entropy and hence will not happen. Thus the necessary condition for equilibrium of an isolated system is that its "Entropy shall be maximum."

 Other forms of second law of thermodynamics

Kelvin-Planck statement : It is impossible to construct a device which, operating in a cycle has the sole effect of extracting heat from a single reservoir and performing equivalent amount of work.

Clausius statement : It is impossible for heat to flow from a cooler body to another hotter body  without the aid of external energy.

 "Study on heat engines is based on the above law"

What is first law of Thermodynamics?

When a definite amount of work is done a certain amount of heat is produced and vice versa.

It can be mathematically expressed as

W = JH

where 'J' is a constant called Mechanical equivalent of heat and 'H' is heat produced. 

But a true version of the law is stated as follows

 “When an amount of heat is supplied to a system a part of it is used in raising internal energy of the system and a part in doing the work.”

                                                      dQ = dU + dW 

 where

dQ - amount of heat supplied ;

  dU - change in internal energy ;

                                                            dW - change in work

 From the first law it could be inferred that it is impossible to derive any work without expenditure of an equivalent amount of energy in some other forms.

 According to first law "The energy of universe remains constant".

 For mathematical calculations it should be kept in mind that heat absorbed by the system should be taken as "positive" and rejected by the system should be taken as "negative".

 Let us now apply first law to some thermodynamic processes.

 i) In an isothermal change dU=0 and dQ = dW; thus in an isothermal change the quantiity of heat absorbed by  a perfect gas is transformed into work by the gas.

 ii) In an adiabatic process, dQ=0 and dU+dW=0 -> dU = - dW

  a) If the system is compressed, work is done on the gas and thus dW is taken as -ve.

                                           Hence  dU = -(-dW) = dW

   b) If the system expands adiabatically 'dW' is positive.

                                           Hence  dU=-(+dW) = -dW

iii) In an adiabatic compression, the decrease in volume is associated with increase in temperature and 

      increase in pressure.