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Consider Ω = αU^(αNV) Use the following steps to find T, U(T), and CV 1. Use quantum mechanics and some combinatorics to find an expression for the multiplicity,Ω , in terms of U, V, N, and any other relevant variables. 2. Take the logarithm to find the entropy, S. 3. Differentiate S with respect to U and take the reciprocal to find the temperature, T, as a function of U and other variables. 4. Solve for U as a function of T (and other variables). 5. Differentiate U(T) to obtain a prediction for the heat capacity (with the other variables held fixed).

Consider Ω = αU^(αNV) Use the following steps to find T, U(T), and CV 1. Use quantum mechanics and some combinatorics to find an expression for the multiplicity,Ω , in terms of U, V, N, and any other relevant variables. 2. Take the logarithm to find the entropy, S. 3. Differentiate S with respect to U and take the reciprocal to find the temperature, T, as a function of U and other variables. 4. Solve for U as a function of T (and other variables). 5. Differentiate U(T) to obtain a prediction for the heat capacity (with the other variables held fixed).

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Consider Ω = αU^(αNV)

Use the following steps to find T, U(T), and CV

1. Use quantum mechanics and some combinatorics to find an expression for the multiplicity,Ω , in terms of U, V, N, and any other relevant variables.

2. Take the logarithm to find the entropy, S.

3. Differentiate S with respect to U and take the reciprocal to find the temperature, T, as a function of U and other variables.

4. Solve for U as a function of T (and other variables).

5. Differentiate U(T) to obtain a prediction for the heat capacity (with the other variables held fixed).

 

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