Thermos Bottle. (a) State and justify how the thermal...

Name: Problem 171, Chapter 2: Problems and Solutions on Thermodynamics and Statistical Mechanics
Uploaded: 2020-06-18T06:32:10-08:00
Duration: 57 s
Channel: David Zhang
Description: Thermos Bottle. (a) State and justify how the thermal conductivity of an ideal gas depends on its density at fixed temperature. (b) A thermos (Dewar) bottle is constructed of two concentric glass vessels with the air in the intervening space reduced to a low density. Why can it act as an insulating container even though the vacuum is not perfect?

Thermos Bottle. (a) State and justify how the thermal conductivity of an ideal gas depends on its density at fixed temperature. (b) A thermos (Dewar) bottle is constructed of two concentric glass vessels with the air in the intervening space reduced to a low density. Why can it act as an insulating container even though the vacuum is not perfect?

Thermos Bottle.
(a) State and justify how the thermal conductivity of an ideal gas depends on its density at fixed temperature.
(b) A thermos (Dewar) bottle is constructed of two concentric glass vessels with the air in the intervening space reduced to a low density. Why can it act as an insulating container even though the vacuum is not perfect?

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Key Concepts

Kinetic Theory of Gases

The kinetic theory explains that in an ideal gas heat is transported as molecules move and collide, with thermal conductivity determined by the product of the number density of molecules, their average speed, and their mean free path. Although a higher density means more carriers of energy, it also results in a shorter mean free path due to more frequent collisions; these two effects cancel each other at a fixed temperature, leading to thermal conductivity that is effectively independent of density.

Vacuum Insulation

Vacuum insulation relies on reducing the amount of material available for heat conduction and convection. By keeping the space between walls at a very low gas density, even an imperfect vacuum minimizes heat transfer because the few remaining molecules have long mean free paths and contribute negligibly to thermal conduction. This drastic reduction in conductive pathways is the reason why such insulation methods are effective in containers like thermos bottles.

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