By Michel Le Bellac
This graduate-level ebook provides a self-contained exposition of primary themes in smooth equilibrium and nonequilibrium statistical thermodynamics. The textual content follows a balanced technique among the macroscopic (thermodynamic) and microscopic (statistical) issues of view. One outstanding characteristic is the big variety of difficulties. easy functions are given in seventy one routines, whereas extra difficult demanding situations are contained in forty seven difficulties, a few of that are invaluable for scholar initiatives.
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Additional info for Equilibrium and Non-Equilibrium Statistical Thermodynamics
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2. What is the entropy change of each of the blocks? What is the total entropy change? 3. We construct a heat engine which uses the two blocks as heat sources. What is the maximum work that can be obtained? What is the final temperature of the two blocks in this case? 5 Stability conditions 1. Establish the following relations at constant N ∂µ ∂V ∂T ∂V V ∂P N ∂V T T ∂P =− CV ∂ T = T S V 2. An experimentalist claims to have found a material with the following properties (i) ∂P ∂V <0 T (ii) ∂P ∂T >0 (iii) V ∂µ ∂V <0 T (iv) ∂T ∂V >0 S Which of the relations above is compatible with the stability conditions?
1. Write the expressions for the differentials dE and dS of the rod internal energy and entropy in the variables (T, L). 2. Calculate the specific heat C L (L , T ) for arbitrary length L. 3. Let the temperature of the rod at length L 0 be T0 . Calculate its entropy S(L , T ) in terms of S(L 0 , T0 ). 4. The rod is in an initial state characterized by L i and Ti . By applying an external force on it, its length is taken adiabatically and reversibly to L f with L f > L i . Give the expression for the final temperature Tf and verify that the lengthening of the rod is accompanied by cooling.
In a quasi-static process, the external pressure, Pext , 18 Thermostatics is infinitesimally close to the internal pressure, P. 1(a)). 1). 5) we see that the quantity (−∂ E/∂ V ) S,N is indeed the pressure, as is T (∂ S/∂ V ) E,N . We emphasize, yet again, the essential point that (for N fixed) conservation of energy or the ‘first law’, dE = d− Q + d− W , is always valid. The equation dE = T dS + d− W , which relies on the notion of entropy and, therefore, the ‘second law’, is valid only for quasi-static processes.