# How many kilograms of ice do you need to cool the water in the bathroom from 17 to 7 degrees.

How many kilograms of ice do you need to cool the water in the bathroom from 17 to 7 degrees. The volume of water is 100 liters. The ice temperature is 0 degrees.

t1 = 17 ° C.

t2 = 7 ° C.

t3 = 0 ° C.

Vw = 100 l = 0.1 m ^ 3.

ρ = 1000 kg / m ^ 3.

Sv = 4200 J / kg * ° C.

ql = 3.4 * 10 ^ 5 J / kg.

ml -?

The amount of heat energy Qw, which must be taken from the water to cool it, is determined by the formula: Qw = Cw * mw * (t1 – t2).

We express the mass of water mw by the formula: mw = Vw * ρ.

Qw = Cw * Vw * ρ * (t1 – t2).

The amount of thermal energy Ql, which is necessary for melting ice and heating water, is expressed by the formula: Ql = ql * ml + Cw * ml * (t2 – t3).

Qw = Ql.

ql * ml + Cw * ml * (t2 – t3) = Cw * Vw * ρ * (t1 – t2).

ml = Cw * Vw * ρ * (t1 – t2) / (ql + Cw * (t2 – t3)).

ml = 4200 J / kg * ° C * 0.1 m ^ 3 * 1000 kg / m ^ 3 * (17 ° C – 7 ° C) / (3.4 * 10 ^ 5 J / kg + 4200 J / kg * ° C * (7 ° C – 0 ° C)) = 11.4 kg. 