How many degrees of delta t the temperature of 10 kg of water taken at a temperature of t2 = 12 C

How many degrees of delta t the temperature of 10 kg of water taken at a temperature of t2 = 12 C increased if m = 5 kg of molten lead was poured into it at the melting temperature?

Given: m1 (water) = 10 kg; t2 (initial water temperature) = 12 ºС; m2 (lead) = 5 kg.

Constants: C1 (specific heat capacity of water) = 4200 J / (kg * ºС); tmelt (temperature of lead melting) = 327.4 ºС; λ (specific heat of fusion of lead) = 25 * 10 ^ 3 J / kg; C2 (specific heat capacity of lead) = 140 J / (kg * ºС).

C1 * m1 * (t – t2) = λ * m + C2 * m2 * (tpl – t).

4200 * 10 * (t – 12) = 25 * 10 ^ 3 * 5 + 140 * 5 * (327.4 – t).

42000t – 504000 = 125000 + 229180 – 700t.

42700t = 858180.

t = 858180/42700 = 20.1 ºС.

Δt = t – t2 = 20.1 – 12 = 8.1 ºС.