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Unformatted text preview: PHYS 333 Winter 2009 Assignment 6 Due: 5:00 pm Friday March 6 Most of these problems are from Schroeders book. Problems 2 and 3 use Tables 4.1, 4.2, 4.3 and 4.4 from the book: they are provided as a separate PDF file for those who need them. 1. Schroeder 4.6. Power of a Carnot engine . Consider a Carnot cycle in which the working subsatnce is at temperature T hw as it absorbs heat from the hot reservoir, and at temperature T cw as it expels heat to the cold reservoir. Assume that the rates of heat transfer are directly proportional to the temperature differences: Q h = K ( T h- T hw ) and Q c = K ( T cw- T c ) Assume also that the time taken for each transfer is the same, so that Q h = Q h t and Q c = Q C t (a) If no new entropy is created during the cycle except during the two heat transfer pro- cesses, derive an equation that relates T h , T c , T hw and T cw . (b) If the time for the two adiabatic processes is negligible, write down an expresion for the power (work per unit time) output of this engine. Use the First and Second Laws to write the power entirely in terms of the four temperatures and the constant K . Show that, using the result of part (a), the power output can be written as P = K 2 1- T C 2 T hw- T h ( T h- T hw ) (c) Show that for fixed values of T h and T c , the power ouptut has a maximum when T hw = 1 2 ( T h + p T h T c ) (d) Show that the corresponding efficiency of the engine is then = 1- q T c /T h (The value of this expression is a much better approximation to the performance of a steam power-plant than is the ideal efficiency = 1- T c /T h .) 2. Schroeder 4.23 and following, somewhat modified....
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- Winter '09