A lump of wet snow weighing 250 g is thrown into water weighing 1 kg at a temperature of 20⁰C.

A lump of wet snow weighing 250 g is thrown into water weighing 1 kg at a temperature of 20⁰C. When all the snow melted, the total temperature was 5 ° C. Determine the amount of water contained in the snowball. The specific heat of melting of snow is 334 kJ / kg, the specific heat of water is 4200 J / kg ∙ ⁰С.

Data: mw (water mass) = 1 kg; tv (water temperature before adding a lump of snow) = 20 ºС; msn (mass of a lump of snow) = 250 g = 0.25 kg; t (total temperature) = 5 ºС.

Constants: according to the condition λsn (specific heat of melting of snow) = 334 kJ / kg = 334 * 103 J / kg; Sv (specific heat capacity of water) = 4200 J / (kg * ºС).

1) Heat given off by cool water to a lump of snow: Q = Sv * mw * (tv – t) = 4200 * 1 * (20 – 5) = 63000 J.

2) The heat given to water from a lump of snow: Q1 = Q – Q2 = Q – Sv * msn * (t – 0) = 63000 – 4200 * 0.25 * (5 – 0) = 57750 J.

3) The mass of water indicated in the snowball: m = mсн – Q1 / λсн = 0.25 – 57750 / (334 * 103) = 0.077 kg = 77 g.

Answer: The snowball contained 77 g of water.