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Heat and Temperature Question: Help with this question is much appreciated! I am especially getting stuck...

Heat and Temperature Question:

Help with this question is much appreciated! I am especially getting stuck on how to find the time in part two. Thank you!

A cylindrical vessel with a radius R and a height R is completely filled with liquid Helium with a density ρh, a heat of vaporization Lh, and a temperature Th. The whole outside of the vessel is kept at a constant temperature To which is higher than Th. Stefan-Boltzmann’s constant can be considered as a given constant.

a) What is the heat flow due to radiation, and in which direction does the heat flow? Assume the vessel has an emissivity e. Express your answer in the given constants. (5 pts)

b) How long will it take for all the Helium to evaporate? Assume that Th is equal to the boiling point of Helium. The pressure in the vessel is kept constant during evaporation (by an open valve). Express your answer in the given constants. (5 pts)

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