Question

Hot tea (water) of mass 0.27 kg and temperature 67 ∘C is contained in a glass of mass 200 g that is initially at the same temperature. You cool the tea by dropping in ice cubes out of the freezer that are at a temperature of – 11 ∘C. What is the minimum amount of ice in you need to make ice tea (final temperature of 0∘C)? Give your answer in kg to two decimal places. The specific heat of ice is 2200 J/kg ∘C, the specific heat of glass is 840 J/kg ∘C and the specific heat of water is 4186 J/kg ∘C. The latent heat of fusion of ice is 334000 J/kg .

Answer 1

To find the minimum amount of ice needed to make ice tea, calculate the heat transferred from the tea to the ice cubes using specific heat and latent heat of fusion formulas.

Step-by-step explanation:

To find the minimum amount of ice needed to make ice tea (final temperature of 0∘C), we need to calculate the heat transferred from the tea to the ice cubes.

First, calculate the heat transferred from the glass of tea using the specific heat formula:

• Q1 = (mass of tea) x (specific heat of water) x (change in temperature of tea)

Next, calculate the heat transferred from the glass using the specific heat formula:

• Q2 = (mass of glass) x (specific heat of glass) x (change in temperature of glass)

Finally, calculate the heat transferred from the ice cubes using the latent heat of fusion formula:

• Q3 = (mass of ice cubes) x (latent heat of fusion of ice)

The total heat transferred from the tea to the ice cubes is given by:

• Qtotal = Q1 + Q2 + Q3

The minimum amount of ice needed to make ice tea is the mass of the ice cubes that will absorb this total heat when they melt.