![]() (Hint: When x is very small, e x ≈ 1 + x.) Is this the result you would expect? Explain. (d) Show that, in the limit T → ∞, the heat capacity is C = N k. (c) Invert the relation you found in part (b) to find the energy as a function of temperature, then differentiate to find a formula for the heat capacity. (The energy is U = q ϵ, where ϵis a constant.) Be sure to simplify your result as much as possible. (b) Use the result of part (a) to calculate the temperature of an Einstein solid as a function of its energy. Explain why the factors omitted from the formula have no effect on the entropy, when N and q are large. (a) Starting with this formula, find an expression for the entropy of an Einstein solid as a function of N and q. In Problem 2.18 you showed that the multiplicity of an Einstein solid containing N oscillators and q energy units is approximately ![]()
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