Find the latent heat of fusion of ice

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SUMMARY

The latent heat of fusion of ice can be calculated using the principle of conservation of energy, specifically through the equation mc(ΔT) = mc(ΔT). In this scenario, the mass of the cup is 0.24g, and the mass of the cup filled with water is 71.16g, leading to a net mass of water of 70.92g. The initial temperature of the water is 21°C, and after the ice melts, the temperature stabilizes at 4°C. The heat lost by the water must equal the heat gained by the ice to melt it, requiring careful accounting of the temperature changes and masses involved.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically heat transfer.
  • Familiarity with the concept of latent heat.
  • Basic knowledge of specific heat capacity calculations.
  • Ability to manipulate algebraic equations for solving physics problems.
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  • Research the specific heat capacity of water and ice.
  • Learn how to apply the conservation of energy principle in thermal systems.
  • Explore detailed examples of calculating latent heat in different materials.
  • Study the effects of temperature changes on phase transitions in substances.
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1. I need to find the latent heat of fusion of ice. The problem scenario is that i have a cup and fill it 1/3 full with water. I then take a cube of ice and put it in the cup. then the cube of ice melts

mass of the cup=.24g
mass of the cup when filled 1/3 with water=71.16g
initial temperature of water in cup=21 celsius
temperature of water after melt=4 celsius
mass after the ice melts-98.88g

2. It has something to do with mc(delta)t
maybe mc(delta)t=mc(delta)t


3. I just don't know where the numbers are plugged in. Please help
 
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Welcome to PF.

You are on the right track.

First of all figure how much heat is contained by the initial water alone. From net mass of water (less the cup) times the temperature drop of that water then would maybe give you what you want, except that after the ice melts you have the additional heating that went into raising the water in the ice up to 4°.

So figure how to account for that.

What's left over must be what was required to melt the ice.
 

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