Chapter seven The second Law of thermodynamics

The direction of thermal phenomena IF a system for some reason or other is not in a state of equilibrium or has been brought out of it and then left alone(this means that it is not subjected to the action of external forces ), experiments show that a transition to an equilibrium state occurs spontaneously. But when equilibrium has already set in, a system, as proved by experiments, cannot by itself return to the initial non-equilibrium state.in other words, the changes in state that occurred in a system while passing into the state of equilibrium cannot take place in the reverse direction whit out any external action. So we can say that the process,

Such as thermal conductivity,diffusion and internal friction, which connected with thermal phenomena are irreversible. It should be remembered that process in which a system constantly remains in a state of equilibrium are called quasi-static. It is quite clear that such process are reversible because all the intermediate states are equilibrium ones.

Definition of entropy We have know that the irreversibility of heat processes itself is connected with the fact that the transition to the equilibrium state is overwhelmingly more probable in comparison with all other transitions. This is why we only observe such changes of state in which a system passes from a less probable to a more probable state. So we define a property S called entropy which has the similar behavior with the probability.

Boltzmann related the entropy S and the thermodynamic probability W by the expression : Where k is boltzmann constant. Entropy is a property of a system, thus it may be expressed in terms of other thermodynamic properties and tabulated just like enthalpy or internal energy. It is indeed tabulated as a function of pressure and temperature for a wild variety of substance.

The entropy of idea gas According to the boltzmann formula, we can get the entropy of idea gas.if we use temperature T and volume V as independent variable, then : Where k is boltzmann constant, N is particle number, m is the mass of the particle.

When there is 1 mol gases, the above formula becomes : Where :

Principle of increase of entropy Entropy in reversible process in a closed system : Entropy in irreversible process in a closed system :

Whatever the process is reversible or irreversible we can suppose there are reversible process between beginning state and final state, then calculate the change of the entropy in this way : If the process is reversible adiabatic one, the entropy changes will be zero. If the process is irreversible and adiabatic, then the entropy must increase.

The second Law of Thermodynamics Four descriptions of the second Law of thermodynamics :  Heat flows from a high temperature to a low temperature in the absence of other effects. This means that a hot body will cool down when brought into contact with a body at a lower temperature and not the opposite.  Tow gases, when placed in an isolated chamber,will mixed uniformly throughout the chamber but will not separate spontaneously once mixed.

 A battery will discharge through a resister releasing a certain amount of energy, but it is not possible to make the reverse of this happen,I.e, to add energy to the resister by heating and, thus,cause the battery to charge itself.  It is not possible to construct a machine or device which will operate continuously while receiving heat from a single reservoir and producing an equivalent amount of work.

In accordance with the descriptions we may tentatively conclude that the second law of thermodynamics has its primary emphasis in an acknowledgment of the unidirectional nature of heat transfer and certain type of energy conversation. The first law of thermodynamics is: Since then, and our equation becomes :

The second law of thermodynamics can be described by the following equations : The sign of equality is fit for reversible process,the sign of inequality is fit for irreversible process.

The second law of thermodynamic is sometimes even expressed in the form of a statement that a perpetual motion machine of the second kind is impossible, just like the first law canbe expressed in the form of the statement that a perpetual motion machine of the first kind is impossible. The second law of thermodynamic also can be described by Kelvin-Plank and Clausius statements, in the later parts we can see the tow statements is equivalent.

Kelvin-Plank and Clausius statements Clausius statements : It is impossible to construct a device which operates in a cycle and whose sole effect is to transfer heat from a cooler body to a hotter body. Heat engine

Kelvin-Plank statements : It is impossible to construct a device which operates in a cycle and produce no other effects than the production of work and exchange of heat with a single reservoir. Heat engine

The equivalence of the Clausius and Kelvin-Plank statements Let us suppose that it would be possible to transfer heat as in (a) in violation of the Clausius statement.To the system (a) we could add the reversible engine as in (b). From energy conservation, the work output of this engine is.The second Law, of clause,dose not prohibit this type of engine. However, the net result of adding the heat engine in (b) is that no net heat is exchanged with the reservoir at and the arrangement is equivalent to the one in (c). The engine in (c) is just the type of device excluded by Kelvin-Plank statement. Thus we have show that a violation of the Clausius statement results in a violation of Kelvin-Plank statement as well.

Carnot ’ s theorem The efficiency of reversible heat engines working at given values of temperatures of the heat source and the heat sink are the same one,it dose not depend on the nature of the working body. The efficiency of a irreversible heat engine working at given values of temperatures of the heat source and the heat sink cannot be greater than that of reversible heat engines at the same heat source and the heat sink.

The Thermodynamic Temperature Scale In previous chapters when considering different ways of measuring temperature, we noted that a serious difficulty is encountered in such measurements. it consist in that the temperature scales established with the aid of various thermometric bodies do not coincide with one another. we have just,however, acquainted ourselves with a property that does not depend at all on the kind of substance and can therefore serve as a faultless thermometric property for establishing a temperature scale, this property is that any substance when used as the working body in a reversible heat engine gives the same efficiency.

Suppose There Are Two Heat Source Temperature Is and Respectively ( and Are Determined by Any Temperature Scales ), According to Carnot ’ s Theorem, We have : the Carnot heat engine absorbs the heat from heat source and gives up to the heat sink, the function can be write as, then : Both the and are depend on temperature scale. Kelvin suppose a new temperature scale,its temperature can be write as, the three phase point of water is K 。 if is proportion to,then,.We suppose that a Carnot heat engine absorbs the heat at the temperature

It should be noted that the temperature scale based on properties of a Carnot machine is called thermodynamic temperature scale. It was proposed by Kelvin whom the scale named. The new scale dose not depend on the kind of substance. And Gives up to the Heat Sink the Heat at the Temperature K,Then We Can Write :

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