A 0.035 kg ice cube at its melting point is dropped into an insulated container of liquid nitrogen. How much nitrogen evaporates if it is at its boiling point of -196 C?
Nitrogen has heat of vaporization of 200000 J/kg
Ice's specific heat is 2100 J/kg*C
Assuming that all of the ice cube's heat energy is used to heat the nitrogen.
Q = m c T = (0.035)(2100)(0- -196) = 14406 J
Latent Heat for Nitrogen (H)
H = m*L = m*200000
The Attempt at a Solution
Since Q = H
14406 = 200000*m
m = 0.072 kg
This is the correct answer.
But what I do not understand is:
How do we know for sure that the ice cube will reach a temperature of -196 C?
This problem feels incomplete. What if the container of nitrogen had 10^1000000000 kg of nitrogen? What if the nitrogen was at 1 K? Clearly, in some cases, that ice cube will not be able to bring the nitrogen to boil. This is not factored into the solution.