Second Law Of Thermodynamic

Second law of thermodynamic

        The limitations regarding the transformation of heat energy into mechanical energy are stated by the second law of thermodynamics. It can be stated in number of ways. The two basic statements were stated by Lord Kelvin and Clausius.

Kelvin Statement:  “It is impossible to to drive a continuous supply of work by cooling a body to a temperature lower than of the coldest of its surroundings.”

               A machine which works on Kelvin’s statement is called as Heat engine, the working of which can be understood by the following flow chart. i.e. a continuous supply of heat can never be obtained from a single supply of heat. The conservation of heat into work is possible only when the working substance works between two different temperatures, it means that heat engine cannot convert all the heat energy into mechanical energy without giving a part of it to the cold body or the sink.

Clausius statement:  “It is impossible to cause heat to flow from a clod body to to a hot body without doing any work.”

               A refrigerator is a machine which conveys heat from a body at lower temperature o a body at higher temperature. This can be achieved only when it is connected by a suitable working substance or external egency which can provide it enough energy so that heat can flow in reverse direction.

A refrigerator is a machine which conveys heat from a body at lower temperature o a body at higher temperature. This can be achieved only when it is connected by a suitable working substance or external egency which can provide it enough energy so that heat can flow in reverse direction.

Equivalence of Kelvin and clausius statement

         Two statements of the second law of thermodyanics seem to be different but the fact is contrary. If any one of the two statements is violated, another one also violates.

        Suppose that Kelvin statement is false, that  it is impossible to construct an engine which takes heat from the source and convert it completely into work and rejects no heat to the sink. It means that source is capable to do work by itself. Thus it will extract heat from the cold body, which provides the basis of such a refrigerator which transfers heat from cold body to the hot bodywithout the expenditure of energy which is contrary to the clausius statement.

Carnot Engine:  Carnot engine is an ideal heat engine which was assumed by Sadi Carnot. It is free from all imperfections of real heat engine, thus its efficiency would be an ideal fficiency and could never be obtained by any real heat engine. Carnot engine consists of a cylinder with ideally heat insulating frictionless piston. Further whose walls are ideally heat insulating and base is ideally heat conducting. An ideal gas is enclosed in the cylinder. For the operation of carnot engine, it is also supposed that source and sink are of infinite capacities.

Carnot Cycle:  The operating cycle of a carnot engine is called carnot cycle. It consist of four processes.

Process 01:  In this process the cylinder is placed on a hot body having temperature T₁. The gas is allowed to expand by decreasing the load on the piston slowly and at the same time some heat Q₁ from the heat reservoir flows into the cylinder, so that its temperature remains constant and its volume change to V₂ from V₁. This expansion is called as isothermal expansion.

Process 02:  In this process the cylinder is placed on an insulatorand the gas continues to expand a little. Since no heat can enter or leave the system, therefore this  expansion is called adiabatic expansion. In this process the temperature of gas decreases from T₁ to T₂ and its volume change to V₃ from V₂.

Process 03:  In this process the cylinder is placed on a cold body at a temperature T₂ and the gas is compressed very slowly by increasing the load on the piston. The temperature of the gas is maintained at T₂ by the transferof heat Q₂ from the gas to the cold reservoir and its volume change to V₄ from V₃. This compression is called isothermal compression.

Process 04:  In this process the cylinder is once again placed on the insulator and the gas is compressed until it attains its initial state. In this process no heat can enter or leave the system, therefore this compression is called adiabatic compression. The temperature of the gas increases from T₂ to T₁ and its volume comes back to V₁ from V₄.

        If a graph is plotted between volume and pressure of the carnot cycle a loop is obtained. Curve AB and CD are the isothermal where as curve BC  and DA are the adiabatic.

Efficiency of heat engine:  The ratio between output and input is called efficiency,

Efficiency = output/input

Efficiency = workdone / heat absorbed

Entropy:  Entropy of a system is the measure of the molecular disorder. It is also defined as the measure of the unavailability of useful energy in the system. Mathematically change in entropy is defined as the heat transferredto the system at the constant absolute temperature,

∆S = ∆Q/T   (S.I unit is joule per Kelvin)

The change in entropy is taken as positive when heat is added to the system and taken as negative when heat is removed from the system. In any process, molecular disorder of the system either increases or remains constant, which is expressed in the form of a law called “the law of increase of entropy” which states that “All natural processes always take place in such a direction so as to cause increase the entropy of the system and surrounding.”

          The law of increase of entropy is a direct result of the second law of thermodynamic, so the second can be also stated as “when an isolated system undergoes a change, the disorder of the system, either increases or remains constant.”