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tdog123
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Homework Statement
Ina light bulb, billions of electrons flow through the tungsten wire bumping around, causing the filament to glow hot. Hot tungsten evaporates slowly, so its initial thickness profile r(x, t=0) can change over time. Consider a volume V of tungsten, with N bonds total, each requiring energy E to break. We will (rather incorrectly) assume that a constant fraction f of electric power is spent on breaking these bonds, and the remaining (1-f) is spent to heat and illuminate. We will also assume that the temperature remains constant.
a. How much energy must be spent to evaporate a volume dV?
b. As the wire evaporates over time, does the current increase or decrease? Is there anything in this system that remains constant?
c. Derive an equation governing the thickness r(x, t) of the tungsten wire as a function of position and time. Don't assume that the thickness is uniform.
d. Assume now that the thickness r(x, t) has no x dependence (i.e. we start with a perfectly cylindrical wire). Solver for r(t).
e. plot, and discuss your results
notes:
Since the evaporation happens from the surface, you might find it helpful to think in terms of n = number of bonds per area, instead of number of bonds per volume. It's perfectly ok if you write your answer in terms of n, instead of number of bonds per volume.
Homework Equations
Not that I know of
The Attempt at a Solution
Don't even know how to start with this problem