On a gas burner, it is necessary to melt tin with a mass of m = 0.20 kg at the melting temperature.

On a gas burner, it is necessary to melt tin with a mass of m = 0.20 kg at the melting temperature. Determine the volume of burnt natural gas if the heat loss to the environment is 40%.

mo = 0.2 kg.
q = 0.59 * 10 ^ 5 J / kg.
λ = 4.4 * 10 ^ 7 J / kg.
Efficiency = 40%.
mg -?
The coefficient of performance Efficiency shows how a part of the consumed amount of heat Qs is converted into a useful amount of heat Qp: Efficiency = Qp * 100% / Qs.
Useful amount of heat Qp is the heat that goes to melt tin.
Qп = q * mo, where q is the specific heat of fusion of tin.
The consumed amount of heat Qs is the heat that is released during the combustion of gas.
Qz = λ * mg, where λ is the specific heat of combustion of natural gas.
Efficiency = q * mo * 100% / λ * mg.
mg = q * mo * 100% / λ * efficiency.
mg = 0.59 * 10 ^ 5 J / kg * 0.2 kg * 100% / 4.4 * 10 ^ 7 J / kg * 40% = 0.00067 kg.
Answer: to melt tin, it is necessary to burn natural gas mg = 0.00067 kg.