Find the latent heat of fusion of ice

[soccerawesome]

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

 

[LowlyPion]

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.

 

[nlightner]

The latent heat of fusion of ice is the amount of energy required to change a substance from a solid to a liquid state without changing its temperature. In this scenario, the ice cube is melting in the cup of water, so the latent heat of fusion of ice is the energy that is being transferred from the water to the ice to cause it to melt.

To calculate the latent heat of fusion of ice, we can use the formula Q = m L, where Q is the heat energy, m is the mass of the substance, and L is the latent heat of fusion. In this case, the mass of the ice cube is 71.16g - 98.88g = 27.72g. We also know that the initial temperature of the water is 21 degrees Celsius and the final temperature is 4 degrees Celsius. We can use the specific heat capacity of water, which is 4.186 J/g°C, to calculate the heat energy required to change the temperature of the water from 21°C to 4°C. This can be done using the formula Q = mc(delta)t, where c is the specific heat capacity of water and (delta)t is the change in temperature.

So, the heat energy required to change the temperature of the water is Q = (71.16g)(4.186 J/g°C)(4°C - 21°C) = -582.7 J. The negative sign indicates that the water is losing heat energy.

Next, we can use the formula Q = m L to calculate the latent heat of fusion of ice. We know that Q is -582.7 J, m is 27.72g, and we need to solve for L. Rearranging the formula, we get L = Q/m. So, the latent heat of fusion of ice is -582.7 J / 27.72g = -21.0 J/g. The negative sign indicates that the ice is gaining heat energy.

Therefore, the latent heat of fusion of ice in this scenario is -21.0 J/g. This means that for every gram of ice that melts, 21.0 J of heat energy is transferred from the water to the ice.