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unscientific
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Homework Statement
Find an expression for thermal conductivity using kinetic theory.
Given a vacuum flask of these dimensions, find the heat loss per unit time.
Estimate the time taken for the water to cool down to 40 deg.
Homework Equations
The Attempt at a Solution
Part (a)
[tex] k = \frac {1}{3} C_{mol} n λ <c> [/tex]
Part (b)
Estimate gap to be 0.5cm.
[tex] n = \frac {PV}{RT} =\frac {(10^{-2})(3.3*10^{-4})}{(8.31)(293)} = 1.4 * 10^{-9} [/tex]
Since the the molecular density is so low, we can effectively say the mean free path is the gap. [tex] λ ≈ 0.5 cm [/tex] (Not sure if this is right, but if the molecule would crash into the other end of the fask before it hits the molecule, then the mean free path should definitely be in the order of magnitude of the gap, right?)
Heat Capacity of air should be same order of magnitude as water;
[tex] C_{mol} ≈ 10^3 J K^{-1} [/tex]
[tex] <c> ≈ 400 m s^{-1} [/tex]
Estimate Temperature gradient ≈ ΔT/5cm) = 8000 K/m
Together, [tex] k ≈ 9.3*10^{-7} [/tex] So, [tex] P = JA = 4.69 * 10^{-4} [/tex]
Part (c)
Time taken = [tex] \frac {Q}{Power} = 1.79*10^8 s = 6 years [/tex]
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