What amount of energy is required to melt a 26.9 g piece of ice at 0oC?

The heat of fusion of ice = 333 Jg-1

Heat required to melt the ice = J

What amount of energy must be removed from 120 g of water to cool it from 72.1oC to 12.4oC?
Specific heat of water = 4.184 JK-1g-1

Enter the heat as a negative amount (heat removed from a system is by convention always negative).
Heat removed to cool the water = J

What is the final temperature after a 26.9 g piece of ice is placed into a styrofoam cup containing 120 g of hot water at 72.1oC. The mass of the ice, and the mass and initial temperature of the hot water are the same as in the two previous parts of this question.

Final temperature =

#1. mass ice x deltaHfusion = ?

#2. q = mass x specific heat x (Tfinal-Tinitial) = ?

#3.
You can put the pieces together.
heat to melt ice + heat to raise T of melt from zero C to final T + heat lost by hot water going to lower final T.

To find the amount of energy required to melt the ice, we can use the formula:

Heat required to melt the ice = mass of ice * heat of fusion of ice

Given:
Mass of ice = 26.9 g
Heat of fusion of ice = 333 J/g

Plugging in the values, we get:

Heat required to melt the ice = 26.9 g * 333 J/g

Simplifying the calculation, we find that the amount of energy required to melt the ice is 8939.7 J.

To find the amount of energy that must be removed from the water to cool it, we can use the formula:

Heat removed to cool the water = mass of water * specific heat of water * change in temperature

Given:
Mass of water = 120 g
Specific heat of water = 4.184 J/gK
Change in temperature = 72.1oC - 12.4oC = 59.7oC

Plugging in the values, we get:

Heat removed to cool the water = 120 g * 4.184 J/gK * 59.7oC

Simplifying the calculation, we find that the amount of energy required to cool the water is 29900.88 J.

To find the final temperature after placing the ice into the hot water, we can use the principle of conservation of energy. The energy lost by the hot water will be gained by the ice as it melts.

So we can set up the equation:

Heat lost by the hot water = Heat gained by the ice

Using the formula for heat:

Heat lost by the hot water = mass of water * specific heat of water * change in temperature

Given the same values as in the previous part:

Heat lost by the hot water = 120 g * 4.184 J/gK * (72.1oC - final temperature)

Using the formula for heat required to melt the ice:

Heat gained by the ice = mass of ice * heat of fusion of ice

Given the same values as in the first part:

Heat gained by the ice = 26.9 g * 333 J/g

Setting the two equations equal to each other and solving for the final temperature:

120 g * 4.184 J/gK * (72.1oC - final temperature) = 26.9 g * 333 J/g

Now we can solve for the final temperature.