# How much water can be heated from 10 degrees C to boiling by burning alcohol weighing 50 g.

How much water can be heated from 10 degrees C to boiling by burning alcohol weighing 50 g. Is the efficiency of a spirit lamp 50%?

To calculate the mass of water heated in an alcohol lamp, we use the formula: η = Sv * mw * (t – t0) / (qc * mc) and mw = η * qc * mc / (Sv * (tc – t0)).

Constants and variables: η – efficiency of the spirit lamp (η = 50% = 0.5); qс – heat of combustion of alcohol (qс = 27 * 106 J / kg); mc is the mass of alcohol (mc = 50 g = 0.05 kg); Cw – heat capacity of water (Cw = 4200 J / (kg * K)); tк – temp. boiling (tк = 100 ºС); t0 – temp. water before heating (t0 = 10 ºC).

Calculation: mw = 0.5 * 27 * 106 * 0.05 / (4200 * (100 – 10)) = 1.79 kg.

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