The vessel contains 1 kg of water taken at t = 10 ° C. How much steam needs to be added

The vessel contains 1 kg of water taken at t = 10 ° C. How much steam needs to be added so that the water temperature is 50 ° C.

Initial data: m1 (mass of water in a vessel) = 1 kg; t0 (water temperature in the vessel) = 10 ºС; t (equilibrium temperature) = 50 ºС.

Reference values: tboil (water vapor temperature) = 100 ºС; C (specific heat) = 4200 J / (kg * K); L (specific heat of vaporization) = 2.3 * 10 ^ 6 J / kg.

С * m1 * (t – t0) = L * m2 + C * m2 * (tboil – t) = m2 * (L + C * (tboil – t)).

m2 = С * m1 * (t – t0) / (L + C * (tboil. – t)) = 4200 * 1 * (50 – 10) / (2.3 * 10 ^ 6 + 4200 * (100 – 50 )) = 0.067 kg = 67 g.