What is the equation of second law of thermodynamics?

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by Utsavsterbon

2015-01-13T05:51:35+05:30

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The second law of thermodynamics tells us the following:

Kelvin Planck statement :  No process is possible whose sole result is the absorption of heat from a heat reservoir, and the complete conversion of the heat (thus absorbed) into work.

Clausius statement : No process is possible whose sole result is the transfer of heat from a colder object to a hotter object.
This means that some work will be required to be done in the process.  Some rejection of heat is also possible.

The second law implies that the efficiency of a heat engine is less than 1.  There can be no  perfect heat engine, no perfect heat pump or perfect refrigerator.

A reversible heat engine with multiple cycles on an ideal gas as the system is called Carnot machine.  It operates between two temperatures.

efficiency of use of energy =  η =  W / Q₁ =  1  -  T₂ / T₁    < 1
W = work done,    Q₁ = heat absorbed by system at temperature T₁
Q₂ = Q₁ - W  = heat rejected / released into reservoir at temperature T₂

efficiency in using energy =  η = W / Q₁  =  [ 1 - Q₂ / Q₁ ],

η =  < 1
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A refrigerator is like a heat pump.  It extracts Q₂ from cold substances at temperature T₂, and work W is done on the system - refrigerant liquid - gas.

Q₁ = W + Q₂  = heat released to the heat reservoir at outside air temperature T₁

Coefficient of performance of refrigerator = α = Q₂ / W = Q₂ / (Q₁ - Q₂)
α = T₂ / ( T₁ - T₂ )

The second law states that ,  α < ∞.