Thermodynamics, Statistical Physics, and Quantum Mechanics

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air molecules isabout Therefore, there are very fewcollisions

between themoleculesthattravel from one wall of the thermos to the other.

We can assumethat we are in the Knudsenregime of ( is the distance

between thewalls). In thisregime thethermalconductance is proportional

to the pressure (if it isindependent ofthe pressure). Let usassume

that after amolecule strikes the wall, it acquires the temperature of the

wall. Initiallyafter ithits the wall,a molecule willtakeaway the energy

where we can take for air The number ofmoleculesstriking

the inner wallper timeinterval dt is

where is the concentration ofmolecules and istheiraverage velocity

(seeProblem 4.14). The power due to thethermalconductance is

We can substitute and

Then(S.4.9.4)becomes

So, we can see thatradiationloss has about the sameorder ofmagnitude as

thermal conductance at these parameters. Therefore the properties of the

thermos can only beimprovedsignificantly bydecreasingboth theemissiv-

ity and the residual pressure between thewalls. The energy dissipated is

equal to theenergy change of the mass of the tea:

THERMODYNAMICS AND STATISTICAL PHYSICS