Determine the minimum volume of ice taken at 0 degrees, which should be added to water, the mass of which is 170 g

Determine the minimum volume of ice taken at 0 degrees, which should be added to water, the mass of which is 170 g, and the temperature is 15 degrees, in order to lower its temperature to 0 degrees.

The specific heat of melting of ice λ = 330 kJ / kg. The specific heat capacity of water is c = 4200 J / (kg × oC). The amount of heat corresponding to the cooling of water with a mass of MB = 0.17 kg from 15 ° C to 0 ° C (with a temperature difference ΔT = 15 ° C):

Q = c MV ΔT = 4200 × 0.17 × 15 = 10710 J.

On the other hand:

Q = λ Ml,

where Ml is the mass of ice, kg.

Ml = Q / λ = 10710 / 330,000 = 0.0325 kg.

The density of ice is ρ = 917 kg / m3, which means that the required minimum volume of ice is:

Wl = Ml / ρ = 0.0325 / 917 = 0.000035442 m3 = 35.44 cm3.