An iron box weighing 200 grams contains 100 grams of lead at a temperature of 27 degrees.

An iron box weighing 200 grams contains 100 grams of lead at a temperature of 27 degrees. What mass of natural gas needs to be burned to melt the lead. consider that 40% of the energy is spent on heating the box, which can be released during complete combustion of the gas.

mw = 200 g = 0.2 kg.

mw = 100 g = 0.1 kg.

Сж = 460 J / kg * ° C.

Сw = 140 J / kg * ° C.

λ = 4.4 * 10 ^ 7 J / kg.

q = 25 * 10 ^ 3 J / kg.

t1 = 27 ° C.

t2 = 327 ° C.

k = 40%.

m -?

The amount of heat Qw, which goes to heating the lead, is expressed by the formula: Qw = Qg * (100% – k) / 100%.

Qw = Cw * mw * (t2 – t1) + q * mw.

Qg = λ * m.

Ssv * msv * (t2 – t1) + q * msv = λ * m * (100% – k) / 100%.

m = (Mw * mw * (t2 – t1) + q * mw) * 100% / λ * (100% – k).

m = (140 J / kg * ° C * 0.1 kg * (327 ° C – 27 ° C) + 25 * 10 ^ 3 J / kg * 0.1 kg) * 100% / 4.4 * 10 ^ 7 J / kg * (100% – 40%) = 0.0000025 kg.

Answer: it is necessary to burn gas m = 0.0000025 kg.