Question

Why second law of thermodynamics is called directional law?

Answer 1

Consider a system and its surroundings. The first law of thermodynamics is defined as,

'The work of a system for any adiabatic process connecting two end states depends only on the end states'

Mathematically speaking,

E2-E1= Q-W

For eg., A block of ice is kept in a room. Take ice as a system and your room as a surrounding. The room is at 25 deg C. What is actually happening here? 

It is obvious that 'heat is getting transferred from room to the ice  resulting in the melting of ice' . 

Let us use the first law to try to justify the obvious answer.

Since no work is done on/by the system, we get W=0. Say, E2 and E1 corresponds to state of cold water and ice respectively. Therefore the above equation simplifies to,

E2-E1=Q.-------case 1
E final- E initial = Q; 

E final= Energy state of cold water
E initial= Energy state of bulk of ice
+ve sign denotes that heat is transferred from room to ice

With this expression, we can say that ' heat is getting transferred from ice to room  resulting in the melting of ice'. This mathematical expression seems to be accurate, but it is not. We can write the above equation as,

E1-E2= -Q. ------case 2
E final - E initial = -Q

E final= Energy state of bulk of ice
E initial= Energy state of cold water
-ve sign dentotes that heat is transferred from cold water to room.

Now with the final mathematical expression, we can say that 'heat must have transferred from cold water to room  resulting in the formation of ice'

But, there is no such process existing in our universe.  You may debate 'Then, what's happening in a refrigerator?' In refrigerator, we are giving WORK to accomplish the task (ie. Creating ice from cold water by transferring heat from cold water to room). On the contrary, our final expression says that we don't need to work to accomplish such a process. Isn't that a big mistake? Thus, the first law simply fails and provides us with two answers.

The first law does not tell anything about the directionality of process (ie. energy transfer from cold water to surrounding (or) surrounding to ice). It simply quantifies the energy of a system. To overcome this we are using the second law of thermodynamics.

(There are two major statements of the second law. For this article, I am considering Claussius statement.) 

The second law states that, ' It is impossible to devise a process whose sole result is the transfer of heat from a cold reservoir to a hotter one' 

This law implies that we need some sort of WORK to accomplish the process of heat transfer from cold to hot reservoirs. Thus, this statement eliminates the second case (Heat must have transferred from cold water (cold reservoir) to room (hot reservoir), resulting in the formation of ice)  which we discussed above. This statement helps us to identify the proper direction of flow of energy (here, thermal energy). So the second law goes by the terminology 'directional law of nature'.

Now you can firmly justify the obvious answer ('heat is getting transferred from room to the ice resulting in the melting of ice') which we guessed before, using  the second law of thermodynamics.

When it comes to mathematical notation of the second law, people use a terminology called ENTROPY. The law goes like this 

'Change in entropy of the universe cannot be negative'. I suggest further reading to know about it.