A glass of water at a temperature of 24 ° C was placed in the freezer. In 5 min. the water temperature dropped to 16 ° С.

A glass of water at a temperature of 24 ° C was placed in the freezer. In 5 min. the water temperature dropped to 16 ° С. How many more minutes will it take until all the water completely freezes if the rate of heat release is the same? The specific heat capacity of water is 4180 J / (kg • ° С), the specific heat of solidification is 332.4 kJ / kg.

t1 = 24 ° C.

t2 = 16 ° C.

t3 = 0 ° C.

T1 = 5 min = 300 s.

C = 4180 J / kg * ° С.

q = 332.4 kJ / kg = 332400 J / kg.

T2 -?

Let’s find the cooling capacity of the refrigerator N from the equality: C * m * (t1 – t2) = N * T1.

N = C * m * (t1 – t2) / T1.

Let’s write down the heat balance equation for the second case: C * m * (t2 – t3) + q * m = N * T2.

T2 = (C * m * (t2 – t3) + q * m) / N = (C * m * (t2 – t3) + q * m) * T1 / C * m * (t1 – t2) = (C * (t2 – t3) + q) * T1 / C * (t1 – t2).

T2 = (4180 J / kg * ° C * (16 ° C – 0 ° C) + 332400 J / kg) * T1 / 4180 J / kg * ° C * (24 ° C – 16 ° C) = 3582 s.

Answer: the water in the glass will completely freeze after T2 = 3582 s.