What is the final temperature if 500 g of ice at a temperature of 0 ° C are immersed in 4 liters

What is the final temperature if 500 g of ice at a temperature of 0 ° C are immersed in 4 liters of water at a temperature of 30 ° C?

Data: m1 (ice mass) = 500 g = 0.5 kg; t0 (initial ice temp.) = 0 ºС; V (volume of water) = 4 l = 4 * 10 ^ -3 m ^ 3; t1 (initial water temperature) = 30 ºС.

Reference data: λ (specific heat of melting of ice) = 3.4 * 10 ^ 5 J / kg; C (specific heat capacity of water) = 4200 J / (kg * K); ρ (water density) = 1000 kg / m ^ 3.

λ * m1 + С * m1 * (t2 – t0) = C * ρ * V * (t1 – t2).

3.4 * 10 ^ 5 * 0.5 + 4200 * 0.5 * t2 = 4200 * 1000 * 4 * 10 ^ -3 * (30 – t2).

170,000 + 2100t2 = 504000 – 16800t2.

18900t2 = 334000.

t2 = 334000/18900 = 17.67 ºС.