2001AugQualTHERM - Ben Sauerwine Practice for Qualifying...

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Ben Sauerwine Practice for Qualifying Exams Thanks to Ben B. for this solution. Near absolute temperature , the tension F in a rubber band is given by: 0 T () 0 2 L L aT F = where L is the stretched length, is the unstretched length, and a is a constant. When , the heat capacity at constant length is: 0 L 0 L L = bT C L = (a) Find the entropy for temperatures T near in terms of its value at and . ( T L S , ) 0 T 0 T 0 L L T L T T L L L T L T F L S T F L S FdL SdT PdL SdT dL L F dT T F dA Maxwell T C T S dL L S dT T S dS L T S S L T F P = = = = + = = + = 0 : , , Then, () () 0 2 0 0 0 0 2 , , 2 2 LL L aT bT L T S S Integrate dL L L aT dT T C dS L L aT T F L L + + = + = =
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(b) If one starts at and and stretches the insulated rubber band quasi-
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2001AugQualTHERM - Ben Sauerwine Practice for Qualifying...

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