hw6 - PHYSICS 420 THERMAL PHYSICS J. D. Maynard READING...

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PHYSICS 420 THERMAL PHYSICS J. D. Maynard READING ASSIGNMENT: Reif, Chapter 5 Homework #6 Due Lecture 33 You are on your honor to work on this on your own, or get hints from Professor Maynard or the Teaching Assistant only. 1. In a temperature range near absolute temperature T, the tension force F of a stretched plastic rod is related to its length L by the expression F = aT 2 ( L - L 0 ) where a and L 0 are positive constants, L 0 being the unstretched length of the rod. When L = L 0 , the heat capacity C L of the rod (measured at constant length) is given by the relation C L = bT, where b is a constant. (a) Write down the fundamental thermodynamic relation for this system, expressing dS in terms of dE and dL. (b) The entropy S ( T, L ) of the rod is a function of T and L. Compute ( ∂S/∂L ) T . (c) Knowing S ( T 0 , T 0 ) , Fnd S ( T, L ) at any other temperature T and length L. (It is most convenient to calculate Frst the change of entropy with temperature at the length L 0 where the heat capacity is known.) (d) If one starts at T = T i and L = L i and stretches the thermally insulated rod quasi- statically until it attains the length L f , what is the Fnal temperature T f ? Is T f larger or smaller than T i ? (e) Calculate the heat capacity C L ( T, L ) of the rod when its length is L instead of L 0 . (f) Calculate S ( T, L ) by writing S ( T, L ) - S ( T 0 , L 0 ) = [ S ( T, L ) S ( T 0 , 0 , L )] + [ S ( T 0 , L ) - S ( T 0 , L 0 )] and using the result of part (e) to compute the Frst term in the square brackets. Show that the Fnal answer agrees with that found in (c). 1
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2. The fgure illustrates a soap flm (shown as cross-hatched) supported by a wire Frame. Because oF surFace tension the flm exerts a Force 2 σl on the cross wire. This Force is in such a direction that it tends to move this wire so as to decrease the area oF the flm. The quantity σ is called the surFace tension oF the flm and the Factor 2 occurs because the flm has two surFaces. The temperature depen-
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hw6 - PHYSICS 420 THERMAL PHYSICS J. D. Maynard READING...

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