- #1
binbagsss
- 1,268
- 11
Homework Statement
I have ##E(w)=w^3(e^{\beta\bar{h}w}-1)^{-1}##,
where ##\beta=K_{B}T##, ##K_{B}## boltzman constant
Homework Equations
Need to solve ##\frac{dE(w)}{dw}=0##
The Attempt at a Solution
[/B]
##k=\beta\bar{h}##:
##\frac{dE(w)}{dw}=3w^2(e^{kw}-1)^{-1}+w^3(e^{kw}-1)^{-2}ke^{kw}(-1)##
##=\frac{3w^{2}(e^{kw}-1)-kw^3e^{kw}}{(e^{kw}-1)^2}##
##\implies w^2(e^{kw}(3-kw)-3)=0##
##w\neq 0 \implies e^{kw}(3-kw)-3=0##
Is this right so far? I don't know how I'd solve this now...?
Many thanks .