1. The problem statement, all variables and given/known data A vacuum flask of radius r and length l consists of two concentric cylinders separated by a narrow gap containing a gas at pressure 10^-2 Nm^-2. The liquid in the flask is at 60 degrees Celcius and the air outside is at 20 degrees celcius. Estimate the rate of heat loss by conduction. 2. Relevant equations κ = 1/3 Cmolecule n λ <v> λ = ( sqrt(2) * n * σ) ^ -1 p = 1/3 nm <v2> pV = nkbT J = - κ ∇T where n is molecules per unit volume. 3. The attempt at a solution κ is independent of pressure so the equation is still valid. Cv per mol is 3/2 R for an ideal gas. So if I divide by avagadro's I will get heat capacity per molecule. <v> = sqrt( 8KBT / m pi) The gas in the "vacuum" is air, so mainly nitrogen, so m = 14. For the temperature of the "vacuum" gas, as it is definitely between 293K and 333K it does not matter exactly. So now we just need the mean free path. We can estimate the collision cross section as 2a^2 where a is the atomic radius. Then we can find n either by using the equation for pressure or the ideal gas equation n = p / KBT Still left with ∇T unknown which seems like a dead end.