How much kerosene must be burned in order to heat 10 kg of water at 20 degrees C to a boil and turn

How much kerosene must be burned in order to heat 10 kg of water at 20 degrees C to a boil and turn 1 kg of it into steam?

mw = 10 kg.

t1 = 20 ° C.

t2 = 100 ° C.

λk = 4.6 * 10 ^ 7 J / kg.

qw = 2.3 * 10 ^ 6 J / kg.

Cw = 4200 J / kg * ° C.

mk -?

The amount of heat Qk, which is released during the combustion of kerosene, is determined by the formula: Qk = λk * mk, where λk is the specific heat of combustion of kerosene, mk is the mass of kerosene that has burned.

The amount of heat Qw, which is necessary for heating and evaporating water, is determined by the formula: Qw = qw * mw + Cw * mw * (t2 – t1), where Cw is the specific heat capacity of water, mw is the mass of water, t1, t2 are the initial and final temperature, qw – specific heat of vaporization of water.

qw * mw + Cw * mw * (t2 – t1) = λk * mk.

mk = qw * mw + Cw * mw * (t2 – t1) / λk.

mk = 2.3 * 10 ^ 6 J / kg * 10 kg + 4200 J / kg * ° C * 10 kg * (100 ° C – 20 ° C) / 4.6 * 10 ^ 7 J / kg = 0, 57 kg.

Answer: it is necessary to burn mk = 0.027 kg of kerosene.