# Solve Fusion & Einstein Homework: Energy Output & Mass Conversion

• Sastronaut
In summary, assuming that 80kg of hydrogen fuel is available, the average human could potentially have 5.04x10^16 J of energy through fusion. This would allow the body to operate for approximately 1.06x10^9 years.
Sastronaut

## Homework Statement

The energy output of an average person is about 121 Watts. Suppose the average human has a mass of 80 kg and it could run on fusion power by converting only .7% of its mass into energy.
1) how much energy would be available to the body through fusion?
2) How long could the body operate on fusion power (in years)?

E=mc2

## The Attempt at a Solution

Question involves 1)...i completed the problem, but realized that i may have made an error. in the first step i multiplied 80kg by .007 or .7% to get a value of .56 kg that could be used in fusion. I then plugged that into E=mc^2 and calculated a value of 5.04x10^16 J. Now does anyone think that for one i am instead being asked to calculate what energy is available if the average human could use its whole weight (80Kgs) in fusion? The rest of my work is bellow i would greatly appreciate if someone could give it a once over! thanks pf!

unknown burned = 121W/5.04x10^16J/kg = approx. 2.401x10^-15 kg/s

Now does anyone think that for one i am instead being asked to calculate what energy is available if the average human could use its whole weight (80Kgs) in fusion?
Relax - the problem is assuming that 80kg of hydrogen fuel is available to power the body.
In 4H->He fusion, only 0.7% of the proton mass is converted to energy - then all the fuel is converted into He: none left to burn.

1 person

## 1. What is fusion and how does it relate to energy output?

Fusion is a process where two or more atomic nuclei combine to form a heavier nucleus, releasing a large amount of energy. This energy is harnessed to produce electricity, making fusion a potential source of clean and renewable energy.

## 2. How does Einstein's famous equation E=mc^2 relate to mass conversion in fusion?

Einstein's equation states that energy (E) and mass (m) are equivalent and can be converted into each other. In fusion, when two atomic nuclei combine, a small amount of mass is converted into a large amount of energy, following this equation.

## 3. What factors affect the energy output in fusion reactions?

The energy output in fusion reactions is affected by factors such as the type of fuel used, the temperature and density of the plasma, and the confinement time of the reaction. The higher the temperature and density, the more energy will be released.

## 4. How is the energy output calculated in fusion reactions?

The energy output in fusion reactions is calculated using the formula E=mc^2, where E is the energy released, m is the amount of mass converted, and c is the speed of light. The mass converted can be determined by measuring the change in mass of the reactants and products of the fusion reaction.

## 5. What are the challenges in achieving a sustainable fusion reaction with high energy output?

Some of the challenges in achieving a sustainable fusion reaction with high energy output include the difficulty in controlling and sustaining the high temperature and density required for fusion, managing the plasma instabilities, and finding suitable materials to withstand the extreme conditions inside a fusion reactor.

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