The temperature of 5 kg of water increased from 7 ° C to 53 ° C when a heated iron weight was lowered into it.

The temperature of 5 kg of water increased from 7 ° C to 53 ° C when a heated iron weight was lowered into it. Determine the weight of the weight if, after lowering it into water, the weight of the weight dropped from 1103 ° C to 53 ° C. The specific heat capacity of water is 4200 J / (kg ° C), and that of iron is 460 J / (kg ° C).

Given:
m1 = 5 kilograms is the mass of water;
T1 = 7 degrees Celsius – initial water temperature;
T2 = 53 degrees Celsius – final water temperature;
c1 = 4200 J / (kg * C) – specific heat of water;
T3 = 1103 degrees Celsius – initial temperature of iron;
T4 = 53 degrees Celsius – the final temperature of iron;
c2 = 460 J / (kg * C) – specific heat of iron.
It is required to determine the mass of the iron weight m2 (kilogram).
According to the laws of thermodynamics, the amount of heat spent on heating the water will be equal to the amount of heat released when the weight is cooled:
Q1 = Q2;
c1 * m1 * (T2 – T1) = c2 * m2 * (T3 – T4);
m2 = c1 * m1 * (T2 – T1) / (c2 * m2 * (T3 – T4)) = 4200 * 5 * (53 – 7) / (460 * (1103 – 53)) = 21000 * 46 / (460 * 1050) = 966000/483000 = 2 kilograms.
Answer: the mass of an iron weight is 2 kilograms.