Energy from D-T fusion and U-235 fission

Mass defect of D-T fusion

Reaction: $D + T \rightarrow He + n$

$$\begin{aligned} m_{in} &= 2.014102 + 3.016049 = 5.030151\ \text{u} \\ m_{out} &= 4.002603 + 1.008665 = 5.011268\ \text{u} \\ \Delta m &= 0.018883\ \text{u} \end{aligned}$$ $$E = \Delta m \times 931.5 = 0.018883 \times 931.5 = 17.59\ \text{MeV}$$

Energy per kg of D-T fuel

One reaction uses 5.030 u of fuel, i.e. 1 kg holds $\dfrac{1000\ \text{g}}{5.030\ \text{g/mol}} \times N_A = 1.197\times10^{26}$ reactions.

$$E_{fus} = 1.197\times10^{26} \times 17.59 \times 1.602\times10^{-13} = 3.37\times10^{14}\ \text{J/kg}$$

Energy per kg of U-235

Atoms in 1 kg: $\dfrac{1000}{235}\times 6.022\times10^{23} = 2.563\times10^{24}$.

$$E_{fis} = 2.563\times10^{24} \times 200 \times 1.602\times10^{-13} = 8.21\times10^{13}\ \text{J/kg}$$

Comparison and coal equivalent

$$\frac{E_{fus}}{E_{fis}} = \frac{3.37\times10^{14}}{8.21\times10^{13}} = 4.1$$

Coal equivalent of 1 kg U-235:

$$\frac{8.21\times10^{13}}{25\times10^{6}} = 3.28\times10^{6}\ \text{kg} \approx 3280\ \text{tonnes}$$

Answer: D-T fusion releases 17.59 MeV; fusion gives $3.37\times10^{14}$ J/kg, about 4.1 times the $8.21\times10^{13}$ J/kg of fission; 1 kg of U-235 is equal to about 3.3 million kg (3280 tonnes) of coal.