diff --git a/src/solutions/1_einstein_model.md b/src/solutions/1_einstein_model.md index 4a32403acaa8cbd37d501f1c4a3941e32b7bc7f4..b17388281bb2a6bb7abb892834ad603feb42e1ff 100644 --- a/src/solutions/1_einstein_model.md +++ b/src/solutions/1_einstein_model.md @@ -77,3 +77,19 @@ $$ where we used $\sum_{n = 0}^{\infty}nr^n = \frac{r}{(1 - r)^2}$. ### Exercise 3: Total heat capacity of a diatomic material. + +1. + +Use the formula $\omega = \sqrt{\frac{k}{m}}$. + +2. + +$E = \frac{N_{^6Li}}{N}\hbar\omega_{^6Li}(2 + 1/2)+\frac{N_{^7Li}}{N}\hbar\omega_{^7Li}(4 + 1/2)$. + +3. + +$E = \hbar\omega_{^6Li}\left(n_B(\beta\hbar\omega_{^6Li}) + \frac{1}{2}\right) + \hbar\omega_{^7Li}\left(n_B(\beta\hbar\omega_{^7Li}) + \frac{1}{2}\right)$. + +4. + +$C = C_{^6Li} + C_{^7Li}$ where the heat capacities are calculated with the formula from Excercise 2.4.