6.7 Second Law of Thermodynamics

6.7 Second Law of Thermodynamics

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 (Fig. 6.8) absorbs a quantity of heat $Q_{1}$ from the heat source at temperature $T_{1}$. It does work $W$ and expels heat $Q_{2}$ 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, i.e.:

In practice, the petrol engine of a motor car extracts heat from the burning fuel and converts a part of this energy to mechanical energy or work and expels the rest to the 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 observations. It can be stated in a number of different ways:

According to Lord Kelvin's statement based on the working of a heat engine:

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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, cannot be made to perform any work. This is true for oceans and our atmosphere which contain a large amount of heat energy but cannot be converted into useful mechanical work. As a consequence of second law of thermodynamics, two bodies at 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.