If 4.2 milligram of mass were to be completely converted into heat energy and this heat is used to raise the temperature of a million kg of water, find the temperature raise (in degree Celsius) of water.

Correct Answer: 90

Solution

$$E = mc^2 = 4.2 \times 10^{-6} \times (3 \times 10^8)^2 = 3.78 \times 10^{11}\text{ J}$$. Taking the specific heat of water as $$4200\text{ J kg}^{-1}\,^\circ\text{C}^{-1}$$, $$\Delta T = \frac{3.78 \times 10^{11}}{10^6 \times 4200} = 90^\circ\text{C}$$.

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