Question

We decided to make an iced latte by adding ice to a 200 mL hot latte at 45 °C. The ice starts out at 0 C. How much ice do we need to add for the final drink to be 10 C? The latent heat of fusion of ice is 335 J/g. Approximate the latte as water. Express your answer in g, without specifying the units.

Answer 1

To lower the temperature of the hot latte to 10°C, you need to add approximately 124.87 g of ice.

Step-by-step explanation:

To find out how much ice you need to add to a hot latte to lower its temperature to 10°C, you can use the formula Q = m × Lf, where Q is the heat transferred, m is the mass of the ice, and Lf is the latent heat of fusion of ice. First, calculate the heat that needs to be transferred:

Q = (200 mL) × (0.997 g/mL) × (45°C - 10°C) × (4.184 J/g°C)

Q = 41,817 J

Next, divide the heat transferred by the latent heat of fusion of ice to find the mass of ice needed:

m = 41,817 J ÷ 335 J/g

m ≈ 124.87 g

Therefore, you need to add approximately 124.87 g of ice to the hot latte to lower its temperature to 10°C.

Answer 2

m = 77.75 g

Step-by-step explanation:

Here we know that at equilibrium the temperature of the system will be 10 degree C

so heat given by hot latte = heat absorbed by the ice

now we have

heat given by latte =
`m s\Delta T`

`Q_1 = (200)(4.186)(45 - 10)`

`Q_1 = 29302 J`

now heat absorbed by ice is given as

`Q_2 = mL + ms\Delta T`

`Q_2 = m(335 + 4.186(10 - 0))`

`Q_2 = m(376.86)`

now by heat balance we have

`Q_1 = Q_2`

`29302 = m(376.86)`

`m = 77.75 g`