How much can the temperature of the water in a $$50\ \text{m} \times 25\ \text{m} \times 2\ \text{m}$$ size pool be raised with the energy released by a single gram of $$^{235}\text{U}$$ Uranium isotope in a nuclear power plant? Assume 47% of the energy ($$200\ \text{MeV}$$ of energy is liberated in the fission of one isotope) is used to heat up the water.<br>(Density of water $$= 1\ \text{g/cm}^3$$, specific heat of water $$= 4.2\ \text{J g}^{-1}\text{K}^{-1}$$)

One gram of $$^{235}\text{U}$$ contains $$\frac{6.02 \times 10^{23}}{235} \approx 2.56 \times 10^{21}$$ nuclei, so it releases $$2.56 \times 10^{21} \times 200 \times 1.6 \times 10^{-13}\ \text{J} \approx 8.2 \times 10^{10}\ \text{J}$$. The useful part is $$0.47 \times 8.2 \times 10^{10} \approx 3.85 \times 10^{10}\ \text{J}$$. The pool holds $$50 \times 25 \times 2 = 2500\ \text{m}^3$$ of water, i.e. $$2.5 \times 10^{9}\ \text{g}$$. Hence $$\Delta T = \frac{3.85 \times 10^{10}}{2.5 \times 10^{9} \times 4.2} \approx 3.67\ \text{K}$$, about $$3.7^\circ\text{C}$$.