In a copper vessel weighing 0.5 kg, heat 2 liters of water taken at a temperature of 10 C.

In a copper vessel weighing 0.5 kg, heat 2 liters of water taken at a temperature of 10 C. To what temperature can water be heated with 50 g of alcohol? The efficiency is considered equal to 50%.

To find the steady-state water temperature, we use the formula: η = (Cm * mc + Sv * mw) * (tx – t0) / (qcp * mcp), from where we express: tx = qcp * msp * η / (Cm * mc + Sv * mv) + t0.

Constants and variables: qcп – beats. the heat of combustion of alcohol (qcp = 27 * 10 ^ 6 J / kg); msp is the mass of alcohol consumed (msp = 50 g = 0.05 kg); η – efficiency of the considered process (η = 50% = 0.5); See – beats. heat capacity of copper (Cm = 400 J / (kg * K)); mс is the mass of the vessel (mс = 0.5 kg); Cv – beats heat capacity of water (C2 = 4.2 * 10 ^ 3 J / (kg * K)); mw is the mass of water (mw = 2 kg (V = 2l)); t0 is the initial temperature of the vessel with water (t0 = 10 ºС).

Calculation: tx = qcp * mcp * η / (Cm * mc + Sv * mv) + t0 = 27 * 1 ^ 06 * 0.05 * 0.5 / (400 * 0.5 + 4.2 * 10 ^ 3 * 2) + 10 = 88.9 ºС.

Answer: The water can be heated up to 88.9 ºС.