Water, taken at a temperature of 20 ° C, boils on the hotplate in 10 minutes. How long does it take for

Water, taken at a temperature of 20 ° C, boils on the hotplate in 10 minutes. How long does it take for all the water to boil off, assuming that the tile is operating at a constant power? The specific heat of vaporization of water r = 2.26 * 10 ^ 6 J / kg, the specific heat of water c = 4200 J / (kg * deg).

t1 = 20 ° C.

t2 = 100 ° C.

С = 4200 J / kg * ° C.

r = 2.23 * 10 ^ 6 J / kg.

T1 = 10 min.

T2 -?

The amount of heat Q1, which is necessary to heat water from t1 to t2, is determined by the formula: Q1 = C * m * (t2 – t1), where C is the specific heat capacity of water, m is the mass of water.

The amount of heat Q2, which is necessary for all the water to boil away, is determined by the formula: Q2 = r * m, where r is the specific heat of vaporization, m is the mass of water.

During its operation, an electric stove emits an amount of heat Q, which is determined by the formula: Q = N * T, where N is the power of the tile, T is its operating time.

Q1 = N * T1.

C * m * (t2 – t1) = N * T1.

N = C * m * (t2 – t1) / T1.

Q2 = N * T2.

r * m = N * T2.

T2 = r * m / N = r * m * T1 / С * m * (t2 – t1) = r * T1 / С * (t2 – t1).

T2 = 2.23 * 10 ^ 6 J / kg * 10 min / 4200 J / kg * ° C * (100 ° C – 20 ° C) = 66.4 min = 66 min.

Answer: for the evaporation of water, time T2 = 66 minutes is required.