Thermodynamics (part-3)

Statement of the second law of thermodynamics

The first law of thermodynamics is a statement of the principle of conservation of heat energy. The second law deals with the condition and possibility of those energy transformations. The second of thermodynamics has been stated by different scientists in different ways. Of all the statements, the one due to Clausius is the most convenient for general use.

Rudolf J. E. Clausius

(1)    Negative stand point (Clausius): “It is impossible for a self-acting machine, unaided by any external agency, to convey heat from one body to another at a higher temperature.”

That is to say, heat will not pass spontaneously from a cold body to a warmer one. In order to make it do so it is necessary to do external work of some sort. In the case of a refrigerator (ammonia ice plant), heat is absorbed from the brine solution at a lower temperature and rejected into water at a higher temperature. This does not happen of its own accord. An external agency (the pump) has to do work in order to achieve this.

(2)    Positive stand point (Edser): “Heat flows of itself from higher to lower temperature.”

Lord Kelvin (1824-1907)

(3)    Lord Kelvin stated the law in the form “It is impossible, by means of inanimate material agency to drive mechanical effect from any portion of matter by cooling it below the temperature of the coolest body of its surroundings.”

This can be readily understood from the fact that a heat engine cannot work already when the temperature of the source and sink are equalized and much more so when the source cools down to a temperature lower than that of the coldest body in the surroundings.

Max Planck (1858-1947) German scientist

     

(4)    Planck stated the law in the form “It is impossible to construct an engine which will work in a complete cycle and produce no effect expects the raising of a weight and the cooling of a heat reservoir.”

(5)    Kelvin and Plank stated the law as follows: “It is impossible to construct an engine which operating in a cycle will produce no effect other than extraction of heat from a reservoir and performance of an equivalent amount of work.”

James Clerk Maxwell (1831–1879)

(6)    Maxwell stated the law as follows: “It is impossible to produce any difference in temperature and pressure in any isolated mass originally at uniform temperature and pressure and pressure without some expenditure of energy.”

Arguments can be advanced to show that these various statements of the second law are essentially equivalent to one another.

It is not possible to prove the law by the experimental verification of a great number of predictions based upon it.

The law explains our failure to utilize the immense quantity of heat energy in our surroundings. For example, we cannot run an engine on the heat content of the oceans because we have no large sink at a lower temperature into which the engine could discharge heat.

It is possible to deduce from the second law of thermodynamics that the reversible engine is the most efficient and that its efficiency depends on the operating temperatures and not on the substance used.

To be more fruitful in application the second law may be stated in precise mathematical way. This requires the introduction of a law new physical quantity called entropy.

Impossibility of perpetual motion machine of the second kind

A cyclic device which would continuously abstract heat from a single reservoir and convert the heat completely to mechanical work is called a perpetual motion machine of the second kind. Such a machine would not violate the first law (the principle of conservation of energy) since it would not create energy but economically it would be just as valuable as if it did so, because of the existence of heat reservoirs such as the oceans or the earth’s atmosphere from which heat could be abstracted continuously at no cost. Hence the second law is sometimes stated, “A perpetual motion machine of the second kind is impossible.”

Carnot’s theorem

Assuming the truth of the second law of thermodynamics, we may deduce two important results which are usually taken together to constitute Carnot’s theorem.

(a)    Working between the same initial and final temperature, no engine can be more efficient than a reversible engine.

(b)    The efficiency of all reversible engines working between the same limits of temperature is the same. 

Entropy

One of the objects of the second law of thermodynamics is to predict the direction in which a thermal process will take place. This is best done by introducing some physical quantity which would be a function of thermodynamic coordinates and which would serve the purpose for determination of the direction of occurrence of a thermal process. In mechanics and in electricity we define the quantities potential and potential energy, for determining the direction of occurrence of an event. In these cases a mass or a charge – as the case may be – moves in such a direction that its potential energy approaches a minimum. In thermodynamical processes we must search for a quantity which tells us about the direction of flow of heat and which could efficiently define the thermodynamical state of any working substance. The required quantity was supplied by Clausius who called it entropy which we denote by the symbol S.

Statement of the second law of thermodynamics in terms of entropy

The statement of the second law of thermodynamics in terms of entropy is in a way, a restatement of the principle of increase of entropy. The law of Clausius may be stated as follows:

“Every physical or chemical process in nature takes place in such a way that the sum of the entropies of all bodies taking part in the process increases. In the limiting case of a reversible process the sum of the entropies remains constant.”