Second law of thermodynamics is law of nature, unarguably one of the most valuable find of mankind. But this topic is somewhat confusing for most of the students and engineers. This video is aimed at describing 2nd law in an engineer's point of view.

## Uses of Second Law

We will start our discussion by going through uses of 2nd law. They are listed below.

### Direction of a Process

### Maximum Possible Thermal Efficiency

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 |

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

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

2nd law has got 2 classical statements, they are self-similar.

### Clausius Statement

### Kelvin-Planck 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 |

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 |

## 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 |

*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

- Entropy transfer - due to heat interaction
- Entropy production - due to effect of irreversibilites

## 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 |

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

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 |

*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.