How much wood must be burned in order to heat 50 liters of water in a 10 kg

How much wood must be burned in order to heat 50 liters of water in a 10 kg iron boiler from 15 degrees Celsius to 65 degrees Celsius?

Vv = 50 l = 50 * 10 ^ -3 m ^ 3.

ρw = 1000 kg / m ^ 3.

Sv = 4200 J / kg * ° C.

Сж = 460 J / kg * ° C.

mk = 10 kg.

t1 = 15 ° C.

t2 = 65 ° C.

λd = 1 * 10 ^ 7 J / kg.

md -?

When burning firewood Q, the amount of heat is released, which is determined by the formula: Q = λd * md, where λd is the specific heat of combustion of firewood, md is the mass of firewood.

The amount of heat Q, which is necessary for heating the pot and water in it, will be determined by the formula: Q = Sv * mw * (t2 -t1) + Szh * mk * (t2 -t1), where Sv, Szh is the specific heat of water and iron , mw, mk – mass of water and pot.

We find the mass of water by the formula: mw = Vw * ρw, where Vw is the volume of water, ρw is the density of water.

Let’s write down the heat balance equation: λd * md = Sv * Vw * ρw * (t2 -t1) + Szh * mk * (t2 -t1).

md = (Sv * Vw * ρw * (t2 -t1) + Szh * mk * (t2 -t1)) / λd.

md = (4200 J / kg * ° C * 50 * 10 ^ -3 m ^ 3 * 1000 kg / m ^ 3 * (65 ° C – 15 ° C) + 460 J / kg * ° C * 10 kg * ( 65 ° C – 15 ° C)) / * 10 ^ 7 J / kg = 1.07 kg.

Answer: it is necessary to burn md = 1.07 kg of firewood.