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Second law of thermodynamics entropy equation examples and applications


Second law of thermodynamics definition

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.

Applications of second law of thermodynamics


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