How many degrees the temperature of 3 liters of boiling water will drop if the same amount of cold water

How many degrees the temperature of 3 liters of boiling water will drop if the same amount of cold water is poured into it at 15. What amount of heat is given off when boiling water is cooled

V1 = V2 = 3 liters = 0.003 m3 – the volume of boiling water and cold water;

t1 = 100 ° Celsius – boiling water temperature;

t2 = 15 ° Celsius – cold water temperature;

c = 4000 J / (kg * C) – specific heat capacity of water;

ro = 1000 kg / m3 – water density.

It is required to determine dt (degrees Celsius) – how much the boiling water temperature will drop and Q (Joule) – how much heat will be released when the water is cooled.

Find the final temperature of the mixture:

Q1 = Q2;

m1 * c * (t1 – t) = m2 * c * (t – t2);

ro * V1 * c * (t1 – t) = ro * V2 * c * (t – t2);

t1 – t = t – t2;

t1 + t2 = t + t;

t1 + t2 = 2 * t;

t = (t1 + t2) / 2 = (100 + 15) / 2 = 115/2 = 57.5 ° Celsius.

That is, the hot water temperature will drop by:

dt = t1 – t = 100 – 57.5 = 42.5 ° Celsius.

Then, the amount of released heat will be equal to:

Q = c * m1 * dt = c * ro * V1 * dt = 4200 * 1000 * 0.003 * 42.5 = 535500 Joules.

Answer: the hot water temperature will drop by 42.5 ° Celsius, the amount of heat released will be 535,500 Joules.