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# First and second Law of thermodynamics

## First law of thermodynamics:

When heat is added to a system there is an increase in the internal energy due to the rise in temperature,an increase in pressure or change in the state.If at the same time,a substance is allowed to do work on its environment by expansion,the heat Q required will be the heat necessary to change the internal energy of the substance from Uin the first state to Uin the second state plus the work W done on the environment.Thus

Q = (U2 –U1) + W

Or

Q = ΔU + W

Thus the change in internal energy ΔU =U2 -U1 is defined as Q -W.Since it is the same for all processes concerning the state,the first law of thermodynamics,thus can be stated as:

“In any thermodynamic process,when heat Q is added to a system,this energy appears as an increase in the internal energy ΔU stored in the system plus the work W done by the system on its surroundings.”

A bicycle pump provides a good example.When we pump on the handle rapidly,it becomes hot due to mechanical work done on the gas,rising thereby its internal energy.

Human metabolism also provides an example of energy conservation.Human beings and other animals do work.When they walk,run,or move heavy objects,work requires energy.Energy is also needed for growth to make new cells and to replace old cells that have died.Energy transforming processes that occur within an organism or named as metabolism.We can apply the first law of thermodynamics:

ΔU =Q – W

to an organism of the human body.Work (W) done will result in the decrease in internal energy of the body.Consequently the body temperature or in other words internal energy is maintained by the food we eat.

## Change in internal energy:

“A function of thermodynamics coordinates whose final value minus initial value is equal to the value of Q +W in the process is called change in internal energy.”

The change in internal energy between equilibrium states i and f is given by:

ΔEint =Eint,f – Eint,i

ΔEint=Q +W

The value of internal energy Eint,i depends only on the coordinate of the state ‘i’.Similarly,Eint,f  depends only on the state of the system and not at all on the path followed.

### Sign convention:

• When heat is supplied to the system,it increases the internal energy,so Q is taken as positive(Q > 0)
• Work done on the system also increases the internal energy ,so it is also taken as positive.(W > 0),In this case first law of thermodynamics is written as:

ΔEint=Q +W

• When heat is rejected by the system,it decreases the internal energy,so it is taken as negative.(Q <0)
• Work done by the system decreases the internal energy ,so it is taken as negative (W <0)

In this case first law of thermodynamics is written as:

ΔEint=Q – W

## Limitations of first law of thermodynamics:

The first law of thermodynamics is a general result that is thought to apply to every process in nature which proceeds between equilibrium states.It tells us that energy must be conserved in every process but it does not tell us whether any process that conserves energy can actually occur.

## Applications of first law of thermodynamics:

“A process in which no heat can enter or leave the system is called adiabatic process.”In an adiabatic process ,there is no transfer of heat across the boundary of the system,so Q=0.According to first law of thermodynamics:

ΔEint=Q +W

Since

Q = 0    ,SO

ΔEint = W

The work done on the system increases the internal energy.

• ### Isothermal process:

“A process in which temperature of the system remains constant is called Isothermal process.”

Since temperature remains constant in isothermal process so the internal energy of the gas must also remain constant so:

ΔEint=Q +W

0 = Q + W

⇒ Q =-W

### Constant volume process:

“The process in which volume of the system remains constant is known as volume process.”

If volume of a gas remains constant,the work done will be zero,thus W=0

So,according to first law of thermodynamics:

ΔEint =Q +W

Since W=0,SO

⇒ Q = ΔEint

In this case all the heat that enters the gas is stored in it as internal energy.

### Cyclic process:

“It is a series of processes after which system returns to its initial state.”It is a three step process.It is a cyclic process,because it starts and ends at the same point.

### Free expansion:

“A process in which a gas goes from one side of the container to the other half initially evacuated is called free expansion.”

## Second law of thermodynamics:

First law of thermodynamics tells us that heat energy can be converted into equivalent amount of work, but it is silent about the conditions under which this conversion takes place. The second law is concerned with the circumstances in which heat can be converted into work and direction of flow of heat.

Before initiating the discussion on formal statement of the second law of thermodynamics, let us analyze briefly the factual operation of an engine. The engine or the system represented by the block diagram, absorbs a quantity of heat Q 1 from the heat  source at temperature T 1. It does work W and expels heat Q  to low temperature reservoir at temperature T 2. As the working substance goes through a cyclic process, in which the substance eventually returns to its initial state, the change in internal energy is zero. Hence from the first law of thermodynamics, net work done should be equal to the net heat absorbed.

W=Q 1_Q 2

In practice, the petrol engine of a motor car extracts heat from the burning fuel and converts a fraction of this energy to mechanical energy or work and expels the rest to atmosphere. It has been observed that petrol engines convert roughly 25% and diesel engines 35 to 40% available heat energy into work.

The second law of thermodynamics is a formal statement based on these observation. It can be stated in a number of different ways.

According to Lord Kelvin’s statement based on the working of a heat engine.

“It is impossible to devise a process which may convert heat, extracted from a single reservoir, entirely into work without leaving any change in the working system.”

This means that a single heat reservoir, no matter how much energy it contains ,can not be made to perform any work. This is true of oceans and our atmosphere which contain a large amount of heat energy but can not be converted into useful mechanical work. As a consequence of second law of thermodynamics, two bodies different temperatures are essential for the conversion of heat into work. Hence for the working of heat engine there must be a source of heat at a high temperature and a sink at low temperature to which heat may be expelled. The reason for our inability to utilize the heat contents of oceans and atmosphere is that there  is no reservoir at a temperature lower than any one of the two.

## Entropy:

The concept of entropy was introduced into the study of thermodynamics by Rudolph Clausius in 1856 to give a quantitative basis for the second law. It provides another variable to describe the state of a system to go along with pressure, volume, temperature and internal energy. If a system undergoes a reversible process during which it absorbs a quantity of heat ΔQ at absolute temperature T, Then the increase in the state variable called entropy S of the system is given by.

Like potential energy or internal energy, it is the change in entropy of the system which is important.

Change in entropy is positive when heat is added and negative when heat is removed from the system. Suppose, an amount of heat Q flow from a reservoir at temperature T a conducting rod to a reservoir at temperature T 2 when T 1>T 2 . The change in entropy of the reservoir, at temperature T 1 which loses heat, decrease by Q/T and of the reservoir at temperature T , which gains heat, increases by Q/T 2. As T > T 2 so Q/T will be greater than Q/T  i.e. Q/T > Q/T 1.Hence:

It follows that in all natural processes where hear flows from one system to another, there is always a net increase in entropy. This is another statement of 2nd law of thermodynamics. According to this law:

“If a system undergoes a natural process,it will go in the direction that causes the entropy of the system plus the environment to increase.”

It is observed that a natural process tends to proceed towards a state of greater disorder. Thus, there is a relation between entropy and molecular disorder. For example an irreversible heat flow from a hot to a cold substance of a system increases disorder because the molecules are initially sorted out in hotter and cooler regions. This order is lost when the system comes to thermal equilibrium. Addition of heat to a system increases its disorder because the increase in average molecular speed and therefore, the randomness of molecular motion. Similarly, free expansion of gas increases its disorder because the molecules have greater randomness of position after expansion than before. Thus in both examples, entropy is said to be increased.

We can conclude that only those processes are probable for which entropy of the system increases or remains constant. The process for which entropy remains constant is a reversible process; whereas for all irreversible processes, entropy of all system increases.

Every time entropy increases, the opportunity to convert some heat into work is lost. For example there is an increase in entropy when hot and cold water are mixed. Then warm water which results cannot be separated into a hot layer and a cold layer. There has been no loss of energy but some of the energy is no longer available for conversion into work. Therefore increase in entropy means degradation  of energy from a higher level where more work can be extracted to a lower level at which less or no useful work can be done. The energy in a sense is degraded, going from more orderly form to less orderly form. eventually ending up as thermal energy.

## Zeroth law of thermodynamic equation:

“According to this law,when two bodies have equality of temperature with third body,then in turn they have equality of temperature with each other.”