Piece of iron put into container with ice

[Lukasz Madry]

Homework Statement

We put 1kg iron of temperature 100 Celsius into container with 1kg of ice, temperature 0 Celsius. What is state of the system after reaching equilibrium? Calculate change of entropy.

Coefficient of melting of ice (c_L) is 330 kJ/kg, coefficient of heat transfer of iron (c_I) is 450 J/(kg*K).

Homework Equations

I don't really know. Heat balance, for sure. Entropy equation - Q = ∫ T dS.
S = c ln(T_f/T_i)
But I'm sure I'm missing something crucial.

The Attempt at a Solution

I tried to compute heat balance:

C_I ( 100 - T_f) = c_L

but this does not work, obviously, since leads to T_f = 100 - c_L/c_I = 100 - 733 which is far below zero temperature.

Another attempt - assume that only part of ice was melted. Let k = c_I 100 / c_L be coefficient that describes how much ice was melted into water. In this case, entropy would be:

S_{iron} = c_I ln(273/373)
S_{ice} = k c_L/273

after substition we can find that it's sum is greater than zero, which is expected.

Is this close to being correct?

 

[scottdave]

So the first thing that I would try to figure is if all the ice melted or not. It seems you determined the answer to that. If you have a container which has ice and liquid water and a piece of iron at equilibrium, what temperature do you think the whole thing will be? If the iron and water are different temperatures, is it at equilibrium? Once you figure the final temperature, then you can figure how much heat transferred from the iron, then go from there.

 

[Lukasz Madry]

Essentialy, energy will flow from iron to ice until iron reaches temperatures of ice OR ice melts down. In this case, iron reaches 0 Celsius way before ice melts down. My only gripe with this is liquid water that keeps appearing - at the beginning it has temperature of ice, but is in contact with iron. It should make heat flow from iron not only to ice, but to this water too. However, ultimately this heat should also reach ice, since ice has temperature of 0 until it totally melts down.

This means that whole thing will be at the temperature of 0 Celsius, and there will be ice, liquid water and iron in the system. Proportions of ice to liquid water are determined by k coefficient I defined in the first post.
Is this correct?

 

[scottdave]

@Lukasz Madry I think you understand how it works.

 

[Lukasz Madry]

Thank you for Your help