# The temperature of water weighing 5 kilograms increased from 7 to 53 degrees when a heated iron weight

The temperature of water weighing 5 kilograms increased from 7 to 53 degrees when a heated iron weight was lowered into it. Find the mass of this weight if, after lowering it into water, its temperature dropped from 1103 to 53 degrees

Given:

m1 = 5 kilograms is the mass of water;

t1 = 7 degrees Celsius – initial water temperature;

t2 = 53 degrees Celsius – the temperature of the water after the weight was lowered into it;

c1 = 4200 J / (kg * C) – specific heat of water;

T1 = 1103 degrees Celsius – initial temperature of the weight;

T2 = 53 degrees Celsius – the temperature of the weight after it was lowered into the water;

c2 = 450 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 given off by the weight is equal to the amount of heat due to which the water is heated:

Q1 = Q2;

c1 * m1 * dt = c2 * m2 * dT;

c1 * m1 * (t2 – t1) = c2 * m2 * (T1 – T2);

m2 = c1 * m1 * (t2 – t1) / (c2 * (T1 – T2)) = 4200 * 5 * (53 – 7) / (450 * (1103 – 53) = 4200 * 5 * 46 / (450 * 1050) = 966000/472500 = 2 kilograms.

Answer: the mass of an iron weight is 2 kilograms.

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