What is Second Law of Thermodynamics ?

Uses of Second Law

Direction of a Process

Most important use of second law is to determine direction of a process. First law of thermodynamics tells the user only about energy transfer, it does not specify in which direction energy transfer will happen for a given condition. Consider following examples.According to first law hot tea can gain heat, mass can go up and mixed gas can become unmixed spontaneously. It is 2nd law of thermodynamics which comes in between and tells in which direction a process is possible spontaneously.

Fig.1 Second law is used to determine in which direction above processes will happen spontaneously

Well, you could argue that you can find out direction of all this processes without using second law (from your intuition). Then what about following process, a chemical reaction.

Fig.2 Second law can even check whether the chemical reaction above is spontaneous or not

Can you say in which direction reaction will go spontaneously from your intuition ? Using 2nd law you can predict even this, you can predict whether the blue atoms and yellow atoms combine together to form a new molecule spontaneously.

Maximum Possible Thermal Efficiency

Another main use of 2nd law is in determining maximum possible thermal efficiency of a given system. 2nd law of thermodynamics puts a limit for maximum performance a system can achieve. For example you can find whats the maximum thermal efficiency possible for a car engine or refrigerator just by knowing its heat interaction temperatures.

Classical Statements of 2nd Law

Clausius Statement

According Clausius statement heat cannot flow from a hot body to cold body without any external work.This is depicted in following figure.

Fig.3 Clausius statement does not permit the process shown here

Kelvin-Planck Statement

Accoriding to Kelvin-Planck statement a heat engine cannot produce work without rejecting some heat to the surrounding. This is depicted in following figure.

Fig.4 Kelvin-Planck statement does not premit the process shown in figure

Clausius Inequality - 2nd Law in a Useful form for Engineers

Clausius and Kelvin-Planck are 2 classical statements of 2nd law, but they are not in a form which is directly useful for engineers.Most useful form of 2nd law is Clausius inequality, It states that cyclic integral of dQ/T along boundary of a cycle will always be less than or equal to zero.

Here temperature T should be in Kelvin.Right hand side of this equation becomes zero when there is no irreversibility present in the cycle, irreversibilities like friction or vertices. Consider following example, a power production cycle.

Fig.5 Clausius inequality applied on a power plant cycle, dotted line represents boundary of the cycle

Here there are 2 heat interactions in the cycle, one at condenser represented by 'c' next is at boiler represented by 'b'. Assuming there are no irreversibilities present and heat interactions are in uniform temperature, then Clausius inequality reduces to

Concept of Carnot Engine

When heat interactions are happening at uniform temperature and irrevesibilities in cycle are zero, such cycle will give maximum possible thermal efficiency.This cycle is known as Carnot cycle. In this aspect the power cycle we just discussed above is an example of Carnot cycle. So thermal efficiency of such a cycle can be written as

Or 2nd law states that a cycle which gives thermal efficiency more than Carnot efficiency is impossible. If somebody approaches you claiming a very high efficiency engine, with efficiency greater than Carnot efficiency you can send him back immediately.

Second Law for a Process - Concept of Entropy

If you want to apply 2nd law for a process the statements derived above which are for cycles are not useful. Consider following cyclic processes, 1st cycle passes through paths A & B and 2nd cycle passes through paths A & C.

Fig.6 Two cyclic processes used to define 2nd law for a process, here process A same for both the cycles

If there is no irreversibitly in the cycle Clausius inequality for the first cycle cycle can be written as

Similarly Clausius inequality for 2nd cycle can be written as

Comparing these two equations one can write

So irrespective of path taken integration of the quantity dQ/T for a reversible process remains same. This is exactly how a property is defined, properties are independent of path taken. We will call this property entropy, denoted by S.So for a reversible process change in entropy can be represented as

Second Law for an Irreversible Process

One can extend 2nd law equation derived for reversible process to an irreversible. In this case a term called entropy production should be added to the equation. Entropy production signifies degree of irreversibilities during the process. So entropy change equation for an irreversible process is

So there could be 2 components for entropy change in an actual process

1. Entropy transfer - due to heat interaction
2. Entropy production - due to effect of irreversibilites

Value of entropy transfer can be either positive or negative but value of entropy production is always positive.

Increase of Entropy Principle

Consider following case, where system is losing some heat to surroundings. We can approach this problem in 2 ways.

Fig.7 Two approaches in solving same problem, second approach states that entropy transfer of universe is zero

In first approach we consider object as system, so system is losing some entropy due to entropy transfer. In second approach we are considering the object and surrounding of the object together as system, means we are considering the universe together. In such an approach there will not be any heat loss from it. Whatever heat interactions are happening is within the universe. So there is no entropy transfer from universe. The general entropy change equation will be simplified as

Since entropy production term is always positive, from above equation it is clear that change of entropy of universe always positive or entropy of universe always increases. This is increase of entropy principle. We will do a sample problem to demonstrate increase of entropy principle. Consider the following case, a hot tea which is in a surrounding whose temperature is less than temperature of tea. Now the question is whether the tea will gain heat or lose heat ?

Fig.8 Whether this tea will gain hear or lose heat ?

First assume the tea is gaining 10J of heat, then change in entropy of universe is

Substituting values in it

This shows that entropy change of universe is negative, that is against 2nd law of thermodynamics. But if the tea loses 10J of heat this will lead to increase in entropy of universe, which means this is a feasible process.

Concept of Gibbs Free Energy

While using increase of entropy principle engineer has to calculate entropy change of surrounding also.In order to over come this difficulty a new property is introduced - Gibbs free energy.

Fig.9 Use of Gibb's free energy change in determining whether this chemical reaction is spontaneous or not

Consider the example shown above, here we want to determine whether the given chemical reaction will occur spontaneously. For this purpose we have to determine entropy change of universe as we did in earlier case. Here entropy change of system and enthalpy change of system are given, so entropy change of surrounding is given by

So entropy change of universe is

This process is spontaneous if

Since T is always positive we can write process is spontaneous if

We will call L.H.S of this equation as another property called Gibbs free energy. So in short a process is spontaneous if

Most of the time it is also convenient to talk in terms of Gibbs free energy. When Gibbs free energy change of system is less than zero it implies entropy change of universe is greater than zero.

Industrial Applications of 2nd Law

Second law of thermodynamics is extensively used in industry to determine direction of a process or a reaction. Most common method to check whether a reaction is spontaneous is to find out change in Gibbs free energy. If this term is negative for a reaction then the process is spontaneous.

Does Entropy Mean Disorder?

The discussions we have done so far were in macroscopic point of view. But there exists a whole different field of thermodynamics where things are viewed microscopically, called as Statistical thermodynamics.Boltzman relation is considered to be one of the pillar statement of statistical thermodynamics, at the same time it is one of the most controversial too. According to this entropy, S and thermodynamic probability, w are related by the relation

The term thermodynamic probability, w deserves special attention. It represents total number of possible microscopic states available to a system, it often referred to as disorder of the system. So according to Boltzman relation as disorder of the system increases entropy increases, or if during a process disorder of the universe increases that process is spontaneous.But always remember statistical thermodynamics is not free of controversies, especially Boltzman relation. For an engineer thermodynamics in classical point of view is enough for his needs.