In a vessel with cold water weighing 3 kg and a temperature of 15 degrees, poured 2 kg

In a vessel with cold water weighing 3 kg and a temperature of 15 degrees, poured 2 kg of boiling water. What is the water temperature? Neglect the heating of the vessel.

Given:

m1 = 3 kilograms is the mass of cold water;

T1 = 15 degrees Celsius – cold water temperature;

m2 = 2 kilograms – the mass of hot water;

T2 = 100 degrees Celsius – hot water temperature;

c = 4200 J / (kg * C) – specific heat capacity of water.

It is required to determine the temperature of the water in the vessel T (degrees Celsius).

The amount of heat that hot water will give up is equal to the amount of heat that cold water will receive.

Q1 = Q2

c * m1 * (T – T1) = c * m2 * (T2 – T);

m1 * T – m1 * T1 = m2 * T2 – m2 * T;

m1 * T + m2 * T = m2 * T2 + m1 * T1;

T * (m1 + m2) = m2 * T2 + m1 * T1;

T = (m2 * T2 + m1 * T1) / (m1 + m2) = (2 * 100 + 3 * 15) / (2 + 3) = (200 + 45) / 5 = 245/5 = 49 degrees Celsius.

Answer: the temperature will be set in the vessel, equal to 49 degrees Celsius.