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Second Law Of Efficiency In Thermodynamics

 A common measure of energy use efficiency is the first law efficiency , n1 . The first law efficiency is defined as the ratio of  the output energy of  the device to the input energy of  the device. The first law is concerned only with the quantities of energy, and disregards in forms in which energy exists. It doesn't also discriminate between the energies available at different temperatures. It is the second law of thermodynamics which provides a means of assigning a quality index to energy. The concept of available energy or energy provides a useful measure of energy quality.

With this concept it is possible to analyze means of minimizing the consumption of energy to perform a given process,  thereby ensuring the most efficient possible conversion of energy for the required task. 

The Second law of  efficiency n2 , of a process is defined as the ratio of the minimum available energy (or energy) which must be consumed to do a task divided by the actual amount of energy consumed in performing the same Task. 




n2 = Min energy intake to perform the given task /  actual energy intake to perform the same task.

or 

n2 = Amin / A.

where A is the availability or energy. 

A power plant converts a fraction of energy A or W max to useful work W. For the desired output of  W, 

Amin = W and  A = W max. 

Here,

I = Wmax - W      and   n2 =  W / Wmax 

Now, 

n1 = W / Q1 = ( W / W max ) * ( Wmax / Q1) 

n1 = n2 * n carnot 

n2 = n1 / n carnot. 

Since Wmax = Q1 ( 1- (To / T )) 

n2 = W / Q(1-(To/T))  = n1 / n carnot 

If work is involved, Amin = W ( desired ) and if heat is involved, Amin = Q (1- (To/T)).

If  solar energy, Qr is available at a reservoir storage Temperature Tr and if Quantity of heat Qa is transferred by the solar collector at Temperature Ta, then 

n1 = Qa / Qr 

and  n2 = energy output / energy input 

n2 = Qa ( 1 - (To/Ta) ) / Qr (1 - (To/Tr))

n2 = n1 (((1-(To/Ta)) / (1- (To/Tr)))


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