Find amount of water at 20 degrees to melt 100 g ice

In summary, the problem asks for the amount of water at 20°C needed to melt 100 g of ice cubes at -18°C, using the specific heat capacity of ice. The equation used is Qwater = cmΔT, and the attempt at a solution involves finding the latent heat (L) by isolating it in the equation. However, the water temperature is not given in the problem statement and is needed for the calculation. The examples in the book use L for materials at 0°C or 100°C, but in this case, L is for the latent heat of fusion of ice and is not affected by the temperature of the water used to melt it.
  • #1
vtl
4
0
This an extra voluntary question on a physics assignment I've already handed in. But I still want to try and figure it out so here goes:


Homework Statement


This is what I'm told: "You take 100 g ice cubes from the freezer. The ice cubes' temperature is -18°C." The specific heat capacity of ice is 2,0 kJ/kg*K.

And then asked: "How big an amount of water at 20°C is required to melt the ice cubes from the freezer?"


Homework Equations


Qwater = cmΔT
Qice = mL

cwater*mwater*∆Twater+mice*Lmelt+cwater*mice*∆Tice=0

The Attempt at a Solution


I assume I need to find L, because in the examples in the book the L's used are for materials at either 0°C or 100°C, which I've isolated:

-Lmelt=(cwater*mwater*∆Twater)/(-mis )+(cwater*mice*∆Tice)/(-mice )

The problem is that I also don't know mwater because that's what the problem asks me to find. Will any amount of 20°C hot water melt the ice cubes eventually or something?
 
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  • #2
You don't mention the water temperature in the problem statement. That's needed. You mention 20C later - is that given, or a number out of the air?
in the examples in the book the L's used are for materials at either 0°C or 100°C
What temperature do you think the ice will be at just before it melts?
 
  • #3
That's because there are three questions attached to the problem statement. 20 degrees is the temperature of the water you use to melt the ice.

0 and 100 degrees is not related to the temperature of the ice, but of the water used to melt the ice.Edit: forgot to mention the 20 degrees when I translated the problem.
 
  • #4
vtl said:
0 and 100 degrees is not related to the temperature of the ice, but of the water used to melt the ice.
Then I don't understand what that has to do with L. You wrote
in the examples in the book the L's used are for materials at either 0°C or 100°C
L stands for latent heat, right? The latent heat of fusion of ice is nothing to do with the temperature of the water used to melt it. It's a constant which you can just plug in.
 
  • #5



To find the amount of water required to melt 100 g of ice at -18°C, you can use the following equation:

Qwater = Qice

Where Qwater is the heat absorbed by the water, Qice is the heat released by the ice, and they are equal when the ice has completely melted.

We can use the equation Q = mcΔT to calculate the heat absorbed by the water, where m is the mass of water, c is the specific heat capacity of water (4.18 kJ/kg*K), and ΔT is the change in temperature. In this case, the water starts at 20°C and ends at 0°C, so ΔT = -20°C.

Qwater = mcΔT = (m)(4.18 kJ/kg*K)(-20°C) = -83.6 m kJ

Next, we can use the equation Q = mL to calculate the heat released by the ice, where L is the latent heat of fusion for ice, which is 334 kJ/kg.

Qice = mL = (100 g)(334 kJ/kg) = 33.4 kJ

Now, we can set these two equations equal to each other and solve for m, the mass of water required to melt 100 g of ice.

Qwater = Qice
-83.6 m kJ = 33.4 kJ
m = 33.4 kJ / (-83.6 kJ/m) = -0.4 kg

Since mass cannot be negative, we can conclude that it will take 0.4 kg of water at 20°C to melt 100 g of ice at -18°C. This means that any amount of water less than 0.4 kg will not be enough to melt the ice, and any amount greater than 0.4 kg will be more than enough to melt the ice.
 

1. How much water is needed to melt 100 g of ice at 20 degrees Celsius?

The amount of water needed to melt 100 g of ice at 20 degrees Celsius is exactly 100 ml, since the density of water is 1 g/ml at this temperature. This means that 100 ml of water will have a mass of 100 g, which is the same as the mass of the ice.

2. What is the melting point of ice?

The melting point of ice, or the temperature at which it changes from a solid to a liquid, is 0 degrees Celsius or 32 degrees Fahrenheit. This is a constant value and does not change based on the amount of ice being melted.

3. How does the temperature of the water affect the melting of ice?

The temperature of the water does affect the melting of ice. In order for the ice to melt, the temperature of the water needs to be at or above the melting point of ice, which is 0 degrees Celsius. If the water is too cold, the ice will not melt, and if it is too hot, the ice will melt too quickly.

4. Does the mass of the ice affect the amount of water needed to melt it?

No, the mass of the ice does not affect the amount of water needed to melt it. As mentioned earlier, the amount of water needed to melt 100 g of ice is 100 ml, regardless of the mass of the ice. This is because the density of water remains constant at 1 g/ml at 20 degrees Celsius.

5. What is the specific heat capacity of water and how does it relate to melting ice?

The specific heat capacity of water is the amount of energy required to raise the temperature of 1 gram of water by 1 degree Celsius. This value is 4.18 joules/gram Celsius for water. In the case of melting ice, the specific heat capacity of water plays a role in absorbing the heat energy from the surroundings and converting it into energy to break the bonds between the water molecules in the ice, causing it to melt.

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