(a) Calculate the energy released by the fusion of a 1.00-kg mixture of deuterium and tritium, which produces helium. There are equal numbers of deuterium and tritium nuclei in the mixture. (b) If this process takes place continuously over a period of a year, what is the average power output?

The nuclear fusion reaction process involves combining lighter atomic nuclei to form heavier nuclei, accompanied by the release of considerable amounts of energy. For the specific reaction between deuterium () and tritium (), we observe the formation of a helium atom () and a neutron (). This process happens under extremely high temperatures and pressures, usually found in the core of a star.

To fully appreciate the magnitude of this reaction, one should note that both deuterium and tritium are isotopes of hydrogen, the most abundant element in the universe. Unlike fission, which splits heavy atoms to produce energy, fusion offers a cleaner and virtually limitless source of power, with helium as a non-radioactive byproduct.

Understanding Deuterium-Tritium Fusion

This specific fusion reaction serves as a model for nuclear fusion power, which could revolutionize our energy systems. Practical applications aim to recreate the fusion conditions present in the solar core within controlled environments like tokamaks or inertial confinement systems to harness energy for human use. Efficiently achieving this reaction overcomes significant scientific and engineering challenges, but it promises to be a sustainable and environmentally friendly energy source.

Fundamental to the process of nuclear fusion is the principle of mass-energy equivalence, which starkly reveals the interconnected nature of mass and energy. Evidenced by Einstein's famous equation, ), it is clear that even a tiny amount of mass can be converted into a large amount of energy. This concept is central to the calculation of energy released in nuclear reactions, whether they be fusion or fission.

The total energy (is derived from the difference in mass before and after a reaction (). Since the speed of light () is a considerably large number, even a meager mass difference results in an immense quantity of energy. In the homework exercise, we calculated the energy released from the fusion of 1 kg of a deuterium-tritium mix by applying this formula.

Implications of Mass Differences

Calculating the mass difference between reactants and products allows us to determine the energy outcome of nuclear reactions. This approach underscores the transformative power hidden within the heart of matter; releasing this energy holds the key to potentially power our planet with fusion reactors.

The average power output is the amount of energy transferred or converted per unit time. When discussing nuclear fusion, the average power output from the reaction offers a measure of the energy harnessed continuously over a given period. In practical terms, for a fusion power plant, this would be the metric determining the plant's contribution to the electricity grid over time.

In the homework exercise, after calculating the total energy released from the fusion reaction over a span of one year, we used the relationship between energy, power, and time () to find the average power output. This metric can help compare the performance of different energy sources and plays a vital role in the planning and operation of power systems.

Real-world Application

The concept of average power is critical not only in academic exercises but also in real-life applications. It enables engineers and scientists to extrapolate the usability of fusion energy, predicting how it could sustainably meet energy demands if we manage to harness this power effectively on a large scale.