hello everyone. i need help understanding this statement:

d(lnΩ)/dE = 1/k

so Ω are the posible microstates for enegy E, and the derivative of Ω w.r.t E is 1/k

why?

what i understand so far is: looking at the division of energy of two "connected" systems the energy will divide itself in a way that maximizes the total possible microstates, and since the total number of microstates is: Ω

(where "Ω

E

Ω

and since i want to maximize this i say:

dΩ

so now what? i feel that im close but i cant get there

d(lnΩ)/dE = 1/k

_{b}Tso Ω are the posible microstates for enegy E, and the derivative of Ω w.r.t E is 1/k

_{b}T.why?

what i understand so far is: looking at the division of energy of two "connected" systems the energy will divide itself in a way that maximizes the total possible microstates, and since the total number of microstates is: Ω

_{1}(E_{1})*Ω_{2}(E_{2})(where "Ω

_{1}(E_{1})" means posible microstates at E1 for system 1) this would mean:E

_{t}=E_{1}+E_{2}andΩ

_{t}(E_{t})=Ω_{1}(E_{1})*Ω_{2}(E_{2})and since i want to maximize this i say:

dΩ

_{t}/dE_{t}=0so now what? i feel that im close but i cant get there

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