How much water you need to add at 20c to 100g of hot water at 50c to get water with a temperature of 25 degrees.

Given:

m1 = 100 grams = 0.1 kilograms is the mass of hot water;

T1 = 50 degrees Celsius – hot water temperature;

T = 25 degrees Celsius – the required temperature of the mixture;

T2 = 20 degrees Celsius – cold water temperature;

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

It is required to determine how much cold water m2 (kilogram) should be added to hot water.

According to the law of thermodynamics, the amount of heat given off by hot water during cooling will be equal to the amount of heat received by cold water during heating:

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

m1 * (T1 – T) = m2 * (T – T2);

m2 = m1 * (T1 – T) / (T – T2) = 0.1 * (50 – 25) / (25 – 20) = 0.1 * 25/5 =

0.1 * 5 = 0.5 kilograms (500 grams).

Answer: you need to add 0.5 kilograms of cold water.