A vessel with water is heated on an electric stove from 20 ° C to boiling for 20 minutes. How long does it take

A vessel with water is heated on an electric stove from 20 ° C to boiling for 20 minutes. How long does it take to turn 20% of water into steam at the boiling point with the same operating mode of the tile? specific heat capacity of water 4200 J / (kg 0s) specific heat of primary formation of water 2.3 MJ / kg.

t1 = 20 ° C.

t2 = 100 ° C.

T1 = 20 min = 1200 s.

m2 = k * m1 / 100%.

k = 20%.

C = 4200 J / kg * ° С.

q = 2.3 MJ / kg = 2.3 * 106 J / kg.

T2 -?

The amount of heat Q1, which goes to heating water, is expressed by the formula: Q1 = C * m1 * (t2 – t1).

Let us express the power of the tile N: N = Q1 / T1, where T1 is the heating time of the water.

N = C * m1 * (t2 – t1) / T1.

Let us express the amount of heat Q2 that is spent on the evaporation of water: Q2 = q * m2 = q * k * m1 / 100%.

Let us express the power of the tile N during water evaporation: N = Q2 / T2, where T2 is the evaporation time of water.

N = q * m2 = q * k * m1 / 100% * T2.

C * m1 * (t2 – t1) / T1 = q * k * m1 / 100% * T2.

C * (t2 – t1) / T1 = q * k / 100% * T2.

T2 = q * k * T1 / С * (t2 – t1) * 100%.

T2 = 2.3 * 106 J / kg * 20% * 1200 s / 4200 J / kg * ° C * (100 ° C – 20 ° C) * 100% = 1643 s = 27 min.

Answer: the time after which 20% of water will boil off is T2 = 27 minutes.