A7_s_ - PHYS 258 Thermal Physics Assignment 7 1 Temperature...

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PHYS 258 - Thermal Physics: Assignment 7 1. Temperature and Heat Capacity of an Einstein Solid. (a) [2] Using this result, find a formula for the temperature of an Einstein solid as a function of its energy. Use U = q ε , where is one quantum of energy for an oscillator. (b) [2] Using your result from part (a), solve for the energy, U , as a function of the temperature. What is the limit of U as T 0? What is the average number of quanta of energy in each oscillator ( q/N ) at temperature T ? Observe that under the assumptions stated, this number is always much less than 1 and so kT << . (c) [1] Using your result from part (b), calculate the heat capacity of an Einstein solid in the low temperature limit. Sketch C V /Nk as a function of x=kT/ . (Note that the exponential factor goes to zero faster than 1 /T 2 goes to infinity as T 0). You can do it by hands or in Excel, say plotting 10 point within 0<x<0.2 (we should remember that x is small in this problem – low temperature limit)
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A7_s_ - PHYS 258 Thermal Physics Assignment 7 1 Temperature...

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