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Heat Energy?

5.Spaceman Spiff sits just outside the Milky Way galaxy with a cup of liquid Helium which is at approximately 4K (-269 0C). He has with him a small sphere made entirely of copper which is at a temperature of 219K (-54 0C). After a certain amount of time his copper sphere comes into equilibrium with the liquid Helium. If his sphere has a diameter of 2 cm, a mass density of 8.96 g/cm3, and a specific heat of 0.386 J * K-1 * g-1, and the process of the copper coming into equilibrium with the liquid helium burned off 150g of liquid Helium, what is the latent heat of vaporization of liquid Helium? (assume that 4K is the boiling point of He and there is more than 150g of He)

I assume the copper sphere is placed into the cup of helium and that this problem has nothing to do with radiation but just a simple heat lost by copper = heat gained by helium problem.
Heat lost by Cu = ms(deltaT) = volume x density x s x delta T
=( 4/3 Pi 1^3)(8.96)(.386)(215)

Heat gained by He = mass x latent heat
= 150 x latent heat

Put equal and solve for L

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