How Does the Heat Transfer Rate Affect a Beaker of Liquid Nitrogen?

[Jimmy87]

Homework Statement

The mass of liquid nitrogen in an open beaker is found to have decreased by 46.3 g in 10 minutes. If the s.l.h of vaporisation of nitrogen at its boiling point is 1.99 x 105, at what rate were the surroundings heating the beaker? Why is the heat capacity of the beaker irrelevant?

Homework Equations

E = mc delta T
E = m l

The Attempt at a Solution

I am fine with the numerical answer but can't figure out the last part of the question. I would have thought that the specific heat capacity is relevant. I first thought it was irrelevant because the beaker and liquid nitrogen would be at the same temperature but then I thought surely the beaker must be at a higher temperature than the liquid nitrogen inside otherwise there would be no flow of heat? Also it must be higher because the temperature of the surroundings is higher again there would be a flow of heat to the beaker so the beaker's temperature must be changing?

 

[gneill]

Don't think of the beaker as having a single temperature. It represent a thermal resistance and capacitance in a thermal circuit, and there are fixed temperatures presented at each side. Like any RC "circuit" there will be transient and steady-state conditions. Argue from there.

 

[Jimmy87]

I don't think I quite follow. Do you mean the side of the beaker next to the surroundings had a different temperature to the inside part which is in contact with the liquid nitrogen?

 

[gneill]

I don't think I quite follow. Do you mean the side of the beaker next to the surroundings had a different temperature to the inside part which is in contact with the liquid nitrogen?

Yes. The inside wall will be held at the liquid nitrogen temperature (or very close to it depending upon the coefficient of heat transfer for the materials) while the outside wall is bathed in the outside air at (presumably) room temperature.