Ice Cubes & Liquid Water - Thermodynamics

In summary, the problem involves combining four ice cubes at 0°C and 115g of water at 75°C in an insulated container. The final temperature of the mixture is determined by the heat gained by the ice cubes being equal to the heat lost by the water. The solution involves using the specific heat capacities and latent heat of fusion for ice and water, and results in a final temperature of 21°C.
  • #1
ahaanomegas
28
0

Homework Statement



Four ice cubes at exactly [itex]0 \ { }^{\circ} \text{C}[/itex] with a total mass of [itex]53.5 \ \text{g}[/itex] are combined with [itex]115 \ \text{g}[/itex] of water at [itex]75 \ { }^{\circ} \text{C}[/itex] in an insulated container. If no heat is lost to the surroundings, what will be the final temperature of the mixture?

Homework Equations



No specific formulas. Just basic thermodynamics, as explained in the solution.

The Attempt at a Solution



Magnitude of heat gained by Ice cubes = Magnitude of heat lost by Water
[itex]4m_{\text{one ice cube}}c_{\text{ice}}(T'-T_{\text{0-ice}})=m_{\text{water}}c_{\text{water}}(T_{\text{0-water}}-T')[/itex]
From here, I used the numbers in my book and got the wrong answer [below]. :(
21 Degrees Celsius
 
Last edited:
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  • #2
You mean you end with water and ice at 21°C?
 
  • #3
Yes, Sir, but that's my answer, not the correct one.
 
  • #4
Sigh.

Have you ever seen ice at 21°C?
 
  • #5
Ah! I guess I forgot the latent heat. That was obliviously silly. Thanks for helping me through my silliness! I'll re-try the problem once I can and, hopefully, I'll get it right this time around. :) Sorry and thank you, again.
 

Related to Ice Cubes & Liquid Water - Thermodynamics

1. What is the difference between ice cubes and liquid water?

Ice cubes and liquid water are both forms of water, but they have different molecular structures and physical properties. Ice cubes are solid and have a crystalline structure, while liquid water is a liquid with a more disordered molecular arrangement. Additionally, the temperature at which they exist is different, with ice cubes being at or below 0 degrees Celsius and liquid water being at or above 0 degrees Celsius.

2. How do ice cubes and liquid water interact with their surroundings?

Ice cubes and liquid water are both subject to thermodynamic principles, which govern how energy is transferred between systems. For example, ice cubes will melt when placed in a warm environment because the heat energy from the surroundings is transferred to the ice, causing it to gain enough energy to break its molecular bonds and become liquid water. Similarly, liquid water can freeze when placed in a cold environment because it loses energy to its surroundings, causing its molecules to slow down and form a solid crystal structure.

3. Why do ice cubes float in liquid water?

Ice cubes have a lower density than liquid water, which is why they float. This is due to the unique structure of water molecules, where the hydrogen bonds between them create a lattice structure in solid ice that is less dense than the random arrangement of molecules in liquid water. This property of water is essential for the survival of aquatic organisms, as it allows for a layer of ice to form on the surface of lakes and ponds, insulating the water below and preventing it from freezing solid.

4. Can ice cubes and liquid water exist at the same time?

Yes, ice cubes and liquid water can exist in equilibrium with each other at the melting point of water, which is 0 degrees Celsius. At this temperature, the rate of melting of ice cubes is equal to the rate of freezing of liquid water, so they can coexist without any net change in their amounts. However, any change in temperature or other conditions can shift this equilibrium and cause one form to dominate over the other.

5. How does thermodynamics impact the formation and melting of ice cubes?

Thermodynamics plays a crucial role in the formation and melting of ice cubes. When water freezes into ice cubes, energy is released to the surroundings in the form of heat. This is why the surrounding air or water feels warmer when you put ice cubes in it. On the other hand, when ice cubes melt, they absorb heat energy from their surroundings, making the surrounding temperature cooler. This transfer of energy is essential for maintaining the balance of energy in our planet's atmosphere and oceans.

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