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

On a gas burner, it is necessary to melt tin with a mass of m = 0.20 kg, which is at the melting temperature. Determine the volume of burnt natural gas if the heat loss to the environment was 40%. (Specific heat of combustion of natural gas q = 35.5 MJ / kg, specific heat of fusion of tin λ = 6, 03 – 10 ^ 4 J / kg.)

mo = 0.2 kg.

λ = 6.03 * 10 ^ 4 J / kg.

q = 35.3 MJ / kg = 35.3 * 10 ^ 6 J / kg.

k = 40%.

ρ = 0.8 kg / m3.

Vg -?

The coefficient k of losses to the environment shows that k = 40% of the amount of heat that is released during the combustion of gas goes into the environment and only (100% – k) goes to melting the tin.

Efficiency = 100% – k = 100% – 40% = 60%.

Efficiency = Qо * 100% / Qg.

Qо = λ * mo.

Qg = q * mg = q * Vg * ρ.

Efficiency = λ * mo * 100% / q * Vg * ρ.

Vg = λ * mo * 100% / q * efficiency * ρ.

Vg = 6.03 * 10 ^ 4 J / kg * 0.2 kg * 100% / 35.3 * 10 ^ 6 J / kg * 60% * 0.8 kg / m3 = 0.00071 m3.

Answer: to melt tin, it is necessary to burn natural gas with a volume of Vg = 0.00071 m3.