# Heat of Evaporation

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1. May 29, 2017

### HaoPhysics

1. The problem statement, all variables and given/known data
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

2. Relevant equations
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

3. The attempt at a solution
Since Q = H

14406 = 200000*m
m = 0.072 kg

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.

2. May 29, 2017

### Staff: Mentor

There is an unstated premise that there is more nitrogen than ice.
How would that change the answer?

The problem explicitly states that the nitrogen is at its boiling point. Can you see why this is a necessary condition for you to arrive at an answer? Would information would be missing if the initial temperature was lower?

3. May 29, 2017

### HaoPhysics

Ohhh. I see it now. For some reason I thought the problem simply said, "the generic boiling point of nitrogen is -196 C," and thus was wondering how we knew for sure it would get to -196 C.

If the initial temperature was NOT -196 C, then we would HAVE to know what the mass of nitrogen is to see how much temperature increase occurs correct?

4. Jun 2, 2017

### Staff: Mentor

Correct! You would have to discriminate the heat leading to an increase in temperature to that leading to evaporation.