Fa07-Rev1-Sun - 7B MT1 Sunday Review Session Problems...

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Unformatted text preview: 7B MT1 Sunday Review Session Problems Patrick Varilly and Steven Byrnes 1 Liphardt, Spring 05, Prob 2 In an experiment liquid helium at an initial temperature of 1.0 K is to be cooled further by bringing it into contact with a solid which is initially at a lower temperature T . The heat capacity of the liquid helium may be expressed as c L = aT 3 where a = 0 . 128 J K- 4 , and the heat capacity of the solid may be expressed as c S = bT- 2 where b = 0 . 015 J K. Assume the mixture to be mechanically and thermally isolated from the rest of the universe and no work is done in the process. a) How much heat must leave the liquid helium to cool it from 1.0 K to 0.7 K? b) What must be the initial temperature of the solid, T , if the final temperature of the system, helium (initially at T = 1 . 0 K) plus solid (initially at T = T ), is to be 0.5 K? c) Find the total change in the entropy of the universe during this process. To minimize the chance of math errors, leave this answer in terms of the parameters a and b . 2 A Patrick-and-Steven original! A heat pump has a working substance which is N molecules of a diatomic ideal gas (5 degrees of freedom). Each cycle starts in state “A”, at pressure and volume P A , V A . First, it is cooled isochorically to state “B”, where its pressure is P B < P A . Second, the volume is changed isobarically to V C (now it is in state “C”). Third, the pressure is raised isochorically back to P A (this is state “D”). Finally, it is returned isobarically to state “A”.(this is state “D”)....
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Fa07-Rev1-Sun - 7B MT1 Sunday Review Session Problems...

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