Question

A 100 g ice cube having an initial temperature of 0°C is put into an insulated cup containing 200 g of water. After a long time, all the ice is melted and the remaining water is at 0°C. Assuming no heat flows into or out of the cup, what was the initial temperature of the water?

Answer 1

39.8 °C

Step-by-step explanation:

m = mass of the ice = 100 g

L = latent heat of fusion of ice = 334 Jg⁻¹

M = mass of water = 200 g

`c_(w)` = specific heat of water = 4.2 Jg⁻¹°C⁻¹

`T_(wi)` = initial temperature of water = ?

`T_(wf)` = final temperature of water = 0 °C

Using conservation of heat

Heat gained by ice = heat lost by water

m L = M
`c_(w)` (
`T_(wi)` -
`T_(wf)` )

(100) (334) = (200) (4.2) (
`T_(wi)` - 0 )

`T_(wi)` = 39.8 °C