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Thermal Vacuum

I left hot chocolate overnight in thermal carafe, and now it is vacuum sealed and impossible to open. Help!!!?
I will have a first suggestion, is your carafe microwave safe? If it is put it in the microwave, and put in a cup of water, turn on the microwave for 30 seconds, then remove the carafe and try it, and then 30 seconds etc. until the carafe opens, or the water starts to produce bubbles, if the water in the cup produces bubbles, then there is a danger that if you continue that the carafe could explode. You do have to be very careful trying that and if you are reluctant to try then I do not blame you. I will also suggest something between the two previous suggestions. I would boil water in a pot on the stove, turn it off and sit the carafe in the water, upside down if you can, let is sit for about 10 minutes, using oven mittens try to open the carafe. If it does not work boil the water again and sit the carafe in the water upside down, then try again. It should heat the inside quickly.
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Emission System - Ported & Thermal Vacuum Switches
(a) Why thermos must have vacuum between its walls?
(b) If pressure of gas is reduced by factor of two,
by what factor will thermal conductivity of the gas change?
It doesn't have to, but it helps to minimize convection and conduction. Then the only way heat can get from the inner wall to the outer wall is radiation.
Here's a nice website on the conduction problem.
For an ideal gas, the expression for conductivity of a gas (equation 1 on the link) is independent of pressure. Below a certain threshold density, though, conductivity drops off when the mean free path between collisions becomes as big as the dimensions of your thermos. Then the particles in the gas can't get into any kind of equilibrium and the whole model gets tossed out the window.
mean free path (l) is given by:
l = 1/ (n sigma).
where n is the number density (N/V) and sigma is the collision cross section.
If you know l and sigma = 0.43 nm^2 for air, you can calculate the cutoff density and then use P = (N/V) * kT to get the cutoff pressure.
Edit: so the answer is: it depends. Above the cutoff, conductivity is insensitive to pressure change. Below the cutoff conductivity falls off to the point where conduction will be insignificant compared to radiative heat transfer.

March 6th, 2010
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