# Second Law of Thermodynamics

The first law of thermodynamics defines the mass conservation and energy conservation processes only but can’t define the direction of the processes. Precisely, the first law only defines the quantitative prospect and is bound by the fact that when total energy is constant, any process is possible.

Hence to counter the limitations, the second law is introduced as the quality prospect and defines the direction of flow.

Necessity of formulation of Second law:

The second law was formulated due to the limitations of first law. The necessity can be summarized in following points.

1. In a cyclic process, the first law states that heat transfer is equal to work transfer in any system. But in real-life applications, the device can’t convert all the heat supplied to the required work and need.
2. Another example is that when two bodies are in thermal contact, the heat never flows from the colder body to the warmer without any work done. All these principles must be controlling the behavior of physical systems and the second law defines it via entropy.
3. In a compartment with gas and vacuum, and due to the high-pressure difference, between gas and vacuum, gas enters to the vacuum with its higher pressure. But the reverse process cannot happen but the first law can’t define it.
4. The next example is that we cannot cream from coffee without a chemical process that changes the physical characteristics of the system or its environment. Hence to define reversible and irreversible processes, the second law introduces entropy.

## Statement of second law:

1. During the course of every system, the entropy of the universe increases.
2. It is possible to convert heat into work without producing changes in some parts of the system.

Entropy is defined as the measure of the randomness of a system.  Its origin is from Greece and introduced by Clasius. Larger the randomness of the system, the higher the entropy. And as per the second law, any system can move to the direction in which its entropy increases.

For an isolated system, the entropy of the system remains constant or always increases.

Change in Entropy by Clausius equality: For reversible processes, the line integral is an independent path for reversible processes.

∮dQ/dt=0

## Reversible and Irreversible processes:

Entropy can be used to differentiate the reversible and irreversible processes. During any real processes, entropy change must be from greater than or equal to 0 between state 1 and state 2.

Most of the process involving work transfer are irreversible due to friction.

The process is called reversible process whereas when  S2> S1,       the process is called irreversible process.

Reversible processes idealizations of actual processes. However, we assume it to analyze (since the system and compare to the actual. A reversible process is a process in which the initial conditions of the system and surroundings can be achieved by reverse action such that net entropy is zero. i.e. S2= S1 ,

### Irreversible Process:

In an irreversible process, it’s impossible to obtain the final initial and final states. Internally reversible process: In these processes, the irreversibility does not occur within the system, a system undergoes a series of equilibrium states, and if we reverse the system, the system can achieve the exact same equilibrium states before returning to its initial state.

### Externally Reversible Process

The reversibility does not occur outside the system boundaries.  Transfer between a reservoir and a system is an externally reversible process if the surface of contact between the system and reservoir is at the same temperature.

## Control Mass Formulation of Second Law of Thermodynamics:

### Contribution of heat transfer on Entropy:

The transfer only by heat transfer only not by work transfer is called the Reversible Heat Transfer reservoir.

dW=pdV=0

Then,

dS =  dU/T

As per first law,

dQ= dU+ pdV
dS =  dQ/T

Contribution of work transfer on Entropy:

The transfer only by work transfer only not by heat transfer is called Reversible heat transfer reservoir.

Then, Total Heat is,

### Control Mass Formulation of Second Law of Thermodynamics:

The change in entropy of a control volume minus net entropy change of working substance due to mass transfer is greater than or equal to the sum of heat transfers.

## Carnot Cycle

Carnot cycle is the cycle that has efficiency equal to that of the reversible cycle. There are two adiabatic reversible legs and two isothermal reversible legs:

### Process 1-2

Isothermal heat addition: The heat reservoir is a constant temperature source (or receiver). Heat is added to the working substance and temperature rises whereas pressure decreases and volume increases whereas entropy increases.

### Process 2-3

Isentropic Expansion: After addition of heat, reversible adiabatic process (isentropic expansion process) occurs that is no heat is supplied to the system and work is produced. Entropy remains constant during this process.

### Process 3-4:

The heat is transferred from working substance and rejected to a high temperature sink. The volume decreases, temperature remains constant whereas pressure of the substance increases and entropy decreases.

## Process 4-1:

Further compression of working substance occurs such that the initial state is restored. The pressure increases, volume decreases whereas entropy of the system remains constant whereas temperature increases.

## Heat engine

A Heat Engine is a device which converts heat energy to mechanical work. Heat engines do work by using part of the energy transferred by heat from some source. The heat engine takes Q2 amount of heat from T2 and rejects Q1 to the low-temperature T1.

ῂ=  W/Q

And as per first law,

  ∮dQ= ∮dW
                  Q2 – Q1= W
ῂ = (Q2 – Q1)/ Q2  =   1-Q_1/Q_2

As per the second law,

For a complete cycle, entropy is always zero.

0≥Q_2/T_2 -Q_1/T_1

And for reversible heat engine,

0=Q_2/T_2 -Q_1/T_1
Q_2/T_2 =Q_1/T_1

Then, we get the efficiency as,

ῂ = 1-T_1/T_2

## Heat Pump:

Heat pump is a device which takes heat from low temperature and delivers to high temperature.

And as per first law,

∮dQ= ∮dW

Or,

Q1– Q2= W

And,

COP=  Q_2/( Q_2- Q_1 )

As per second law,

∮dScm ≥∮∑(dQ/dT)cm

For a complete cycle, entropy is always zero.

0≥-Q_2/T_2 +Q_1/T_1

And for reversible heat engine,

0=-Q_2/T_2 +Q_1/T_1
Q_2/T_2 =Q_1/T_1

Then, COP can be calculated as,

COP=  T_2/( T_2- T_1 )

## Refrigerator

A refrigerator is a device that takes heat from low temperature to high temperature (T1 to T2) with the help of extra work. The refrigerator easily maintains the temp of the desired space lower than that of the surrounding.

COP=Q_1/W

And as per first law,

∮dScm ≥∮∑(dQ/dT)cm

For a complete cycle, entropy is always zero.

0≥-Q_2/T_2 +Q_1/T_1

And for reversible heat engine,

0=-Q_2/T_2 +Q_1/T_1
Q_2/T_2 =Q_1/T_1

Then, COP can be calculated as,

COP=  T_1/( T_2- T_1 )

## 1. Kelvin-Planck’s Statement:

It is impossible to construct a heat engine to work in a cyclic process where the sole effect is to convert all the heat supplied to it into an equivalent amount of work.

## 2. Clausius Statement

It is impossible to construct a device to work in a cyclic process whose sole effect is the transfer of a body at a lower temperature to a body at a higher temperature.