Piece of iron put into container with ice

In summary, after putting 1kg of iron of temperature 100 Celsius into container with 1kg of ice, temperature 0 Celsius, the state of the system is equilibrium. The entropy of the system is greater than zero.
  • #1
Lukasz Madry
3
0

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?
 
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  • #2
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.
 
  • #3
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?
 
  • #5
Thank you for Your help
 

Related to Piece of iron put into container with ice

What happens when a piece of iron is put into a container with ice?

When a piece of iron is put into a container with ice, the heat from the iron will transfer to the ice, causing it to melt. This is because iron is a good conductor of heat, meaning it can transfer heat energy easily to other objects.

Does the temperature of the iron affect how quickly the ice melts?

Yes, the temperature of the iron does affect how quickly the ice melts. The higher the temperature of the iron, the faster the heat will transfer to the ice and cause it to melt. This is why warm or hot objects can melt ice faster than cold objects.

What is the process behind the melting of ice when in contact with iron?

The process behind the melting of ice when in contact with iron is called thermal conduction. This is when heat energy is transferred from a warmer object to a cooler object through direct contact. In this case, the heat from the iron is transferred to the ice, causing it to melt.

Will the ice eventually stop melting once it reaches a certain temperature?

No, the ice will continue to melt as long as it is in contact with the iron. This is because the iron will continue to transfer heat energy to the ice, causing it to melt. However, once the ice has completely melted, the temperature of the water may reach a point where it is no longer affected by the heat from the iron.

Can the same effect be observed with other materials besides iron?

Yes, the same effect can be observed with other materials besides iron. Any material that is a good conductor of heat, such as copper or aluminum, will transfer heat energy to the ice and cause it to melt in a similar way. However, materials that are poor conductors of heat, such as plastic, will not have the same effect on the ice.

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