Laws of Thermodynamics, Lecture notes of Thermodynamics

Download Laws of Thermodynamics and more Lecture notes Thermodynamics in PDF only on Docsity! Laws of Thermodynamics 0th Law of Thermodynamics Consider two isolated systems, A and B, which have been allowed to reach equilibrium separately. Now bring these systems into thermal contact with each other. Initially, they need not be in equilibrium with each other. Eventually, the combined system, A+B, will reach a new equilibrium state. Some changes in both A and B will generally have occurred, usually including a transfer of energy. In the final equilibrium state of the combined system we say that the subsystems are in equilibrium with each other. If a third system, C, can now be brought into thermal contact with A without any changes occurring in either A or C, then C is in equilibrium with not only with A but with B also. This postulate may be expressed as: 0th Law of Thermodynamics: If two systems are separately in equilibrium with a third, then they must also be in equilibrium with each other. The zeroth law may be paraphrased to say the equilibrium relationship is transitive. The transitivity of equilibrium conditions does not depend upon the nature of the systems involved and can obviously be extended to an arbitrary number of systems. If three or more systems are in thermal contact with each other and all are in equilibrium together, then any pair is separately in equilibrium is easily demonstrated. If the state of the combined system is in equilibrium, its properties are constant; but if a pair of subsystems is not in equilibrium with each other and are allowed to interact, their states will change. This result contradicts the initial hypothesis, thereby proving the equivalence between the 0th law and its converse. The concept of temperature is based upon the 0th law of thermodynamics. For simplicity, consider three systems (A,B,C) each described by the variables 8pi, Vi, i oe 8A, B, C<<. The condition of equilibrium between systems A and C may be expressed as an equation of the form F1@pA, VA, pC, VCD = 0 which may be solved for pC as pC = f1@pA, VA, VCD = 0 Similarly, the equilibrium between systems B and C yields pC = f2@pB, VB, VCD = 0 so that f1@pA, VA, VCD = f2@pB, VB, VCD Finally, the equilibrium between A and B can be expressed as F3@pA, VA, pB, VBD = 0 If these last two equations are to express the same equilibrium condition, we must be able to eliminate VC from the former equation to obtain fA@pA, VAD = fB@pB, VBD where fA or fB depend only upon the state variables of systems A or B independently. The democracy amongst the three systems can then be used to extend the argument to fC , such that fA@pA, VAD = fB@pB, VBD = fC@pC, VCD for three systems in mutual equilibrium. Therefore, there must exist a state function that has the same value for all systems in thermal equilibrium with each other. For each system, this state function depends only upon the thermodynamic parameters of that system and is independent of the process by which equilibrium was achieved and is also independent of the environment. This function will, of course, be different for dissimilar systems. An empirical temperature scale can now be established by selecting a convenient thermometric property of a standard system, S, and correlating its equilibrium states with an empirical temperature q in the form f@8xS<D = q , where 8xS< represents a complete set of thermodynamic parameters (other than temperature) for the standard system. The equation of state of any test system, A, can now be determined. Maintaining the standard system in a constant state, we vary the parameters of the test system in such a way as to maintain equilibrium between S and A. This set of variations then determines f@8xA<D = q as an equilibrium surface of A. The locus of all points HpA, VAL which remain in equilibrium with S at an empirical temperature q describes a curve in the pV diagram called an isotherm. The 0th law of thermodynamics requires that the form of the isotherms be independent of the nature of the standard system S. If we had chosen a different standard system, S£ , at the same empirical temperature as determined by equilibrium