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Laws of Thermodynamics

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Thermodynamics is a branch of physics which deals with the relation between heat and mechanical energy and its related phenomenon. In earlier days heat was considered as a fluid called caloric which is supposed to be weight-less and that is present in every body. Later on Count Rumford in 1798 found that a large amount of heat was produced by friction and the heat produced by friction was proportional to the work done. Sir Humphrey Davy in his experiment rubbed two blocks of ice in vacuum and found melted due to friction, which disagrees with the idea of caloric as there is no other hot body in surroundings for the fluid to transfer. We observe here generation of heat, when the mechanical work is done on the body. 

The same heat is also generated the ice blocks are directly heated. Thus we understand that heat and work are both forms of energy. James Joule and others later on showed that heat lost or gained in any process could be accounted for an equal amount of work done by the system or on the system. This idea lead to extend the concept of energy to include heat as a form of energy, to apply the law of conservation of energy. We have 3 laws of thermodynamics.
  • Zeroth law of thermodynamics 
  • First law of thermodynamics 
  • Second law of thermodynamics

Zeroth Law of Thermodynamics

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Let us consider two systems A and B separated from each other by thermally insulated wall (one that conducts no heat), but each being in contact of a third system C through a (diathermic) wall which permits heat to pass. Then the system A will be in thermal equilibrium with system C and similarly system B will also be in thermal equilibrium with system C. Now if the adiabatic wall between systems A and B is replaced by a diathermic wall, experiments show that no further change occurs in a system A and B indicating thereby the system A was also in thermal equilibrium with B, This important experimental fact leads to the following general conclusion. " If two systems are in thermal equilibrium with a third system then they must be in thermal equilibrium with each other' .  This statement is called the zeroth law of thermodynamics and forms the basis of concept of temperature. 

All these three systems can be said to possess a property that ensure their being in thermal equilibrium with one another. This property is known as temperature. We may, therefore define the temperature of a system as a property that determines whether or not the system is in thermal equilibrium with the neighbouring systems. It is obvious that if two systems are not in thermal equilibrium, they will be at different temperatures. The law was formulated by R.H.Fowler in 1931. It is formulated long after the first and second laws of thermodynamics. Since it is more fundamental in concept than the other two it is named as 'Zeroth law'.

First Law of Thermodynamics

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Let in a process, an amount dQ of heat be given to the ideal gas and an amount dW of work be done by it. The total energy of the gas increases by (dQ - dW). As a result, the internal energy (random motion of the molecules) of the gas may increase. If dU is the change in internal energy, we have

dQ  =  dU  +  dW.

This equation is the statement of the 'first law of thermodynamics'. In an ideal mono-atomic gas, the internal energy of the gas is simply translational energy of all the molecules. In general, the internal energy may get contribution from the vibrational kinetic energy of molecules, rotational kinetic energy of molecules as well as from the potential energy corresponding to the molecular forces. The above equation hence represents a statement of conservation of energy as applicable to any thermodynamic system however complicated. It should be remembered that when work is done by the system, dW is positive. If work is done on the system dW is negative. When heat is given to the system or heat is absorbed, dQ is positive, If heat is given by the system or heat is evolved, dQ is negative.

If zeroth law defines a property of matter called temperature, teh first law enables us to define a property of a system called internal energy. We can write the above equation as   

dU = dQ - dW.  

In the case of an isolated system, there is no interaction with the surroundings. No work is doe by or on the system, i.e., dQ = 0 and dW = 0.

dU = 0 or U = constant i.e., the internal energy of an isolated system is constant. When the heat supplied is completely converted into work without changing the temperature of the system, the internal energy of the system remains constant i.e., dU = 0.

dQ  =  dW

Second Law of Thermodynamics

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First law of thermodynamics conveys the basic idea of conservation of energy in the thermodynamic system. It relates heat energy and mechanical work. It considers heat as a form of energy (internal energy) to generalise the law of conservation of energy. To explain the lack of reversibility in nature, second law of thermodynamics is formulated. It was first announced by Clausius as follows.

Clausius Statement: " It is impossible for a self acting machine unaided by any external agency of transfer heat from a body at lower temperature to a body at higher temperature" This statement indicates the direction of flow of heat. It can also be stated as heat on its own can not flow from a cold body to a hot body.

Kelvin Statement: " It is impossible by any thermodynamic process which results solely in the removal of heat from a heat reservoir and convert it entirely into work." The statement can be interpreted as no heat engine can convert whole of the heat energy supplied to it into useful work.