Second law of thermodynamics

Experimental evidence suggests strongly that it is impossible to build a heat engine that converts heat completely to work (an engine with 100% thermal efficiency). This impossibility is the basis of one statement of the second law of thermodynamics, as follows:

It is impossible for any system to undergo a process in which it absorbs heat from a reservoir at a single temperature and converts the heat completely into mechanical work, with the system ending in the same state in which it began.

We call this the 'engine' statement of the second law.

The basis of the second law of thermodynamics lies in the difference between the nature of internal energy and that of macroscopic mechanical energy. In a moving body the molecules have random motion, but superimposed on this, is a co-ordinated motion of every molecule in the direction of the body's velocity. The kinetic energy associated with this coordinated macroscopic motion is what we call the kinetic energy of the moving body. The kinetic energy and potential energy associated with the random motion constitute the internal energy.

When a body sliding on a surface comes to rest due to friction, the organized motion of the body is converted to random motion of molecules in the body and on the surface. Since we cannot control the motion of individual molecules, we cannot convert this random motion completely back to organized motion. Only a part of it can be converted, and this is what a heat engine does.

If the second law were not true, we could power an automobile or run a power plant by cooling the surrounding air. Neither of these impossibilities violate the first law of thermodynamics. The second law, therefore, is not a deduction from the first, but stands by itself as a separate law of nature. The first law denies the possibility of creating or destroying energy and the second law limits the availability of energy and the ways in which it can be used and converted.

An alternative statement of the second law of thermodynamics states that, heat flows spontaneously from hotter to colder bodies, never the reverse. A refrigerator transfers heat from a colder to a hotter body, but its operation requires an input of mechanical energy or work. Generalizing this observation, we state:

It is impossible for any process to sole result in the transfer of heat from a cooler to a hotter body.

We call this the 'refrigerator' statement of the second law. Though, it may not seem to be very closely related to the 'engine' statement, the two statements are equivalent. For example, if we could build a refrigerator which does not have an input of work, violating the 'refrigerator' statement of the second law, we could use it in conjunction with a heat engine, pumping the heat rejected by the engine, back to the hot reservoir to be reused. This composite machine shown in the figure (b) shown below, would violate the 'engine' statement of the second law because its net effect would be to take a net quantity of heat Q_H- |Q_C| from the hot reservoir and convert it completely to work W.

Alternatively, if we could make an engine with 100% thermal efficiency, violating the first statement, we could run it using heat from the hot reservoir and use the work output to drive a refrigerator that pumps heat from the cold reservoir to the hot reservoir as shown in the figure (b) below. This composite device would violate the “refrigerator” statement because its net effect would be to take heat Q_C from the cold reservoir and deliver it to the hot reservoir without requiring any input of work. Thus, any device that violates one form of the second law can be used to make a device that violates the other form. If violations of the first form are impossible, so are violations of the second!

The conversion of work to heat, as in friction or viscous fluid flow, and heat flow from hot to cold across a finite temperature gradient, are irreversible processes. The 'engine' and 'refrigerator' statements of the second law state that these processes can be partially reversed. We could cite other examples. Gases always seep spontaneously through an opening from a region of high pressure to a region of low pressure: gases and miscible liquids left to themselves, always tend to mix, not to unmix.

The second law of thermodynamics is an expression of the inherent one-way aspect of these and many other irreversible processes. Energy conversion is an essential aspect of all plant and animal life and of human technology. Hence, the second law of thermodynamics is of utmost fundamental importance to the world we live in.