A mixture containing 22.5 gg of ice (at exactly 0.00 ∘C∘C) and 77.1 gg of water (at 50.9 ∘C∘C) is placed in an insulated container. Assuming no loss of heat to the surroundings, what is the final temperature of the mixture?

The final temperature of the mixture is 21.4°C

Explanation:

Specific heat capacity of water = 1 cal/g°c

Heat loss by water = 77.1 g X 1 cal/g°c X 50.9°c = 3924.39 Cal

Latent heat of fusion of ice = 79.7 g⁻¹

Heat required to melt ice at 0°c = 22.5 g X 79.7 g⁻¹ = 1793.25 Cal

Heat gained by ice from water at a higher temperature, T°c = 22.5 X 1 X T

= 22.5T

Also heat lost by water = 77.1 X 1 X (50.9-T) cal

By calorimetric principle

Heat lost by a hot body = heat gained by a cold body

77.1 X 1 X (50.9-T) = 22.5T + 1793.25

3924.39 - 77.1T = 22.5T + 1793.25

99.6T = 3924.39 - 1793.25

T = 2131.14/99.6

T = 21.4°C

Therefore, the final temperature of the mixture is 21.4°C