How many grams of alcohol do you need to burn in an alcohol lamp to heat 580 g water at 80 ° C on it? The efficiency of the spirit lamp (taking into account heat losses) is 20%. (Specific heat of combustion of alcohol 2.9 107 J / kg, specific heat of water 4200 J / (kg ° C)).
Initial data: m1 (mass of water) = 580 g = 0.58 kg; Δt (change in water temperature) = 80 ºС; η (alcohol lamp efficiency) = 20% or 0.2.
Constant data: according to the condition q (specific heat of combustion of alcohol) = 2.9 * 10 ^ 7 J / kg; C (specific heat of water) = 4200 J / (kg * K).
Let us express the mass of alcohol from the formula for calculating the efficiency of an alcohol lamp: η = С * m1 * Δt / (q * m2), whence m2 = С * m1 * Δt / (η * q).
m2 = 4200 * 0.58 * 80 / (0.2 * 2.9 * 10 ^ 7) = 0.0336 kg or 33.6 g.
Answer: You need to burn 33.6 g of alcohol.
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