Question

50 g of ice at 0°C is added to 300 g of a liquid at 30°C. What will be the final temperature of the mixture when all the ice has melted? The specific heat capacity of the liquid is 2.65 Jg^-1 °C^-1 while that of water is 4.2 J g^-1 °C^-1. Specific latent heat of fusion of ice = 336 Jg^-1.

Answer 1

m₁ = 50 g, t₁ = 0 °C, m₂ = 300 g, t₂ = 30 °C 

Heat energy taken by ice to melt = 50 × 336 J = 16800 J

By law of conservation of energy,

Heat energy given by liquid = Heat taken by water

300 × 2.65 × (30 - t) = 16800 + 50 × t × 4.2

⇒ 23850 - 795 t = 16800 + 210 t

⇒ - 795 t - 210 t = 16800 - 23850

⇒ - 1005 t = - 7050

⇒ t = `7050/1005 = 7.014^circ  "C"`