Water with a mass of 100 g was heated on an alcohol lamp from 16 degrees Celsius to 71 degrees Celsius.

Water with a mass of 100 g was heated on an alcohol lamp from 16 degrees Celsius to 71 degrees Celsius. Alcohol weighing 10 g was burned. Find the efficiency of the installation.

Let water with a mass of m₁ = 100 g = 0.1 kg be heated on an alcohol lamp from a temperature t₁ = 16 ° C to a temperature t₂ = 71 ° C. At the same time, the water temperature increased by Δt = t₂ – t₁ = 71 ° C – 16 ° C = 55 ° C. In this process of heat exchange, alcohol released the amount of heat Q₂ = q ∙ m₂, and water received the amount of heat Q₁ = m₁ ∙ c ∙ Δt. The plant efficiency is η = Q₁ / Q₂ or η = m₁ ∙ c ∙ Δt / (q ∙ m₂). From the condition of the problem it is known that to heat the water, alcohol with a mass of m₂ = 10 g = 0.01 kg was burned. In the reference books we find that the specific heat capacity of water c₁ = 4200 J / (kg ∙ ° C), the specific heat of combustion of alcohol q = 27000000 J / kg. Substituting the values ​​of physical quantities in the calculation formula, we find the efficiency of the installation:

η = 0.1 kg ∙ 4200 J / (kg ∙ ° С) ∙ 55 ° С / (27,000,000 J / kg ∙ 0.01 kg);

η = 0.086 = 8.6%.

Answer: The efficiency of the installation is 8.6%.