There was 50g in the glass. water at a temperature of 20 °. It was filled with 100g. water at a temperature of 80 ° C. What was the temperature of the water in the glass after mixing the water?
mx = 50 g = 0.05 kg.
t1 = 20 ° C.
mg = 100 g = 0.1 kg.
t2 = 80 ° C.
Cw = 4200 J / kg * ° C
When mixed, hot water will give up the amount of heat Qg and cool down to temperature t. Cold water will receive the amount of heat Qx and heat up to the temperature t: Qg = Qx.
The amount of heat Qg, which the hot water will give, is expressed by the formula: Qg = Cw * mg * (t2 – t), where C is the specific heat capacity of the water, mw is the mass of hot water, t, t2 are the final and initial water temperatures.
The amount of heat Qx that cold water will take can be expressed by the formula: Qx = Cw * mx * (t – t1), where Cw is the specific heat capacity of water, mw is the mass of cold water, t, t1 are the final and initial temperatures of cold water.
Cw * mg * (t2 – t) = Cw * mх * (t – t1) – heat balance equation.
mg * t2 – mg * t = mх * t – mх * t1.
mх * t + mg * t = mg * t2 + mх * t1.
t = (mg * t2 + mх * t1) / (mх + mg).
t = (0.1 kg * 80 ° C + 0.05 kg * 20 ° C) / (0.05 kg + 0.1 kg) = 60 ° C.
Answer: the temperature in the glass will be set to t = 60 ° C.