In a vessel with water 500 g at a temperature of 80 degrees, poured 300 g of water at a temperature of 30 degrees which is the established temperature.
mg = 500 g = 0.5 kg.
tg = 80 ° C.
mx = 300 g = 0.3 kg.
tx = 30 ° C.
When mixing water of different temperatures, a process of heat exchange occurs, as a result, water with a higher temperature gives off a certain amount of heat to water with a lower temperature.
Qg = C * mg * (tg – t).
Qx = C * mx * (t – tx).
Qg = Qx.
C * mg * (tg – t) = C * mх * (t – tх) – heat balance equation.
mg * tg – mg * t = mх * t – mх * tх.
mg * tg + mx * tx = mg * t + mx * t.
t = (mg * tg + mx * tx) / (mg + mx).
t = (0.5 kg * 80 ° C + 0.3 kg * 30 ° C) / (0.5 kg + 0.3 kg) = 61.25 ° C.
Answer: the temperature in the vessel is t = 61.25 ° C.
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