In the calorimeter, which contains 1 liter of water at 10 grams of Celsius, 100 grams of water vapor

In the calorimeter, which contains 1 liter of water at 10 grams of Celsius, 100 grams of water vapor was admitted. what water temperature will be established in the calorimeter after the onset of thermal equilibrium.

Vw = 1 l = 10-3 m3.

ρ = 1000 kg / m3.

t1 = 10 ° C.

t2 = 100 ° C.

Sv = 4200 J / kg * ° C.

mp = 100 g = 0.1 kg.

λ = 2.3 * 106 J / kg.

t -?

When the steam condenses and the resulting water cools, the amount of thermal energy Q is released, which is determined by the formula: Q = λ * mp + Sv * mp * (t2 – t).

Water for its heating, the required amount of heat Q, is expressed by the formula: Q = Sv * mw * (t – t1).

mv = ρ * Vv.

λ * mp + Sv * mp * (t2 – t) = Sv * ρ * Vw * (t – t1).

λ * mp + Sv * mp * t2 – Sv * mp * t = Sv * ρ * Vw * t – Sv * ρ * Vw * t1.

λ * mp + Sv * mp * t2 + Sv * ρ * Vw * t1 = Sv * ρ * Vw * t + Sv * mp * t.

t = (λ * mp + Sv * mp * t2 + Sv * ρ * Vw * t1) / Sv * (ρ * Vw + mp).

t = (2.3 * 106 J / kg * 0.1 kg + 4200 J / kg * ° C * 0.1 kg * 100 ° C + 4200 J / kg * ° C * 1000 kg / m * 10-3 m3 * 10 ° C) / 4200 J / kg * ° C * (1000 kg / m * 10-3 m3 + 0.1 kg) = 60 ° C.

Answer: the temperature in the calorimeter will be set to t = 60 ° C.