A nuclear reactor generating plant supplies 53.0 MW of useful power steadily for a year. Assuming that, in addition, twice this power is wasted in heat production, determine the mass (in kilograms) converted to energy in a year at this plant.
Multiply 159* 10^6 W by the number of seconds in a year.
That will give you the energy produced. Divide that by c^2 for the mass loss.
This is about thermodynamics and the Einstein E = m c^2 equation, not quantum physics.
To determine the mass converted to energy in a year at the nuclear power plant, we can use Einstein's famous equation, E=mc², where E represents energy, m represents mass, and c represents the speed of light.
First, we'll calculate the total energy generated by the reactor in one year. Since it supplies 53.0 MW of useful power steadily, we can convert this to energy using the equation
E = P * t
where E is energy, P is power, and t is time. In this case, P equals 53.0 MW, and t equals one year.
Thus, we have:
E = 53.0 MW * 1 year
Now, let's convert the power from megawatts to joules since the SI unit of energy is the joule.
1 MW = 1,000,000 J/s, and 1 year = 365 days * 24 hours * 3600 seconds.
E = 53,000,000 J/s * 365 days * 24 hours * 3600 seconds
Next, we know that twice this power is wasted in heat production, so we need to multiply the calculated energy by a factor of 3:
Total_energy = 3 * E
Finally, to find the mass, we rearrange the equation E=mc² to solve for m:
m = E / c²
where c is the speed of light, approximately 3 x 10^8 m/s.
Now, let's substitute the values and calculate:
Total_energy = 3 * E = 3 * (53,000,000 J/s * 365 days * 24 hours * 3600 seconds)
m = Total_energy / c² = (3 * (53,000,000 J/s * 365 * 24 * 3600)) / (3 x 10^8 m/s)²
Simply the equation and perform the calculation in the numerator:
m = (3 * 53,000,000 J/s * 365 * 24 * 3600) / (9 x 10^16 m²/s²)
Now, we can calculate the final answer for the mass converted to energy in a year at the nuclear power plant.