- #1
learningastronomy
- 15
- 3
- Homework Statement
- A two-state paramagnet has 40 magnetic dipoles. Determine the amount of microstates and macrostates?
- Relevant Equations
- ##\Omega(N,n)=\frac{N!}{n!(N-n)!}## or ##\omega(N_{\uparrow})=\frac{N!}{N_{\uparrow}!N_{\downarrow}!}##
Since this is a two-state paramagnet where N = 40, therefore the microstate is ##40^2##? But I am not sure how to proceed to count the number of macrostates? Because from what I understand of what a macrostate is, shouldn't there a specific outcome to be stated in order to determine how many macrostate there are? For instance suppose we have 40 coins then the number of microstate (all different states of heads and tails) will be ##40^2## but in order to compute macrostate then you will have to explicitly provide the state it is in, for example determine the amount of macrostate of the 40 coins that only have two heads then you can use $$\Omega(N,n)=\frac{N!}{n!(N-n)!}$$ $$\therefore\Omega(40,2)=\frac{40!}{2!(40-2)!}=780?$$ And since the question didn't explicitly provide the macrostate then will it just be the general case of $$\Omega(40,n)=\frac{40!}{(40-n)!}?$$
Is my reasoning correct?
Is my reasoning correct?