Heat of Evaporation: Melting Ice to Boil Nitrogen

[HaoPhysics]

Homework Statement

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

Homework 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

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.

 

[DrClaude]

There is an unstated premise that there is more nitrogen than ice.

This problem feels incomplete. What if the container of nitrogen had 10^1000000000 kg of nitrogen?

How would that change the answer?

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.

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?

 

[HaoPhysics]

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?

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?

 

[DrClaude]

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?

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