A certain nuclear plant generates internal energy at a rate of 3.065 GW and transfers energy out

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A certain nuclear plant generates internal energy at a rate...

A certain nuclear plant generates internal energy at a rate of 3.065 $\mathrm{GW}$ and transfers energy out of the plant by electrical transmission at a rate of 1.000 $\mathrm{GW}$ . Of the wasted energy, 3.0$\%$ is ejected to the atmosphere and the remainder is passed into a river. A state law requires that the river water be warmed by no more than $3.50^{\circ} \mathrm{C}$ when it is returned to the river. (a) Determine the amount of cooling water necessary (in kilograms per hour and cubic meters per hour) to cool the plant. (b) Assume fission generates $7.80 \times 10^{10} \mathrm{J} / \mathrm{g}$ of $235 \mathrm{U} .$ Determine the rate of fuel burning (in kilograms per hour) of $^{255} \mathrm{U} .$

Key Concepts

Energy Conservation

This concept involves understanding how energy is distributed in a system. In many engineering applications, the input energy is partly converted into useful output and partly lost (or wasted) in various forms such as heat. Analyzing energy conservation allows us to account for these energy streams and determine how much energy must be managed or dissipated in processes such as cooling or heating of fluids.

Specific Heat Capacity

Specific heat capacity is a material property that quantifies the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. This concept is crucial when calculating the energy absorbed or released by a fluid subjected to a temperature change, and is essential in determining the necessary mass flow rate of a coolant in thermal management problems.

Mass Flow Rate and Energy Transfer

Mass flow rate refers to the mass of a substance passing through a given cross-sectional area per unit time. When combined with the specific heat capacity and temperature change, it helps determine the rate at which energy is absorbed or released. This concept is key in sizing cooling systems and ensuring that temperature limits are not exceeded in thermal exchange processes.

Nuclear Fission Energy Density

Nuclear fission energy density is a measure of how much energy is released per unit mass of nuclear fuel during fission. It is fundamental in determining the rate at which fuel must be consumed to sustain a given power output. This concept connects the microscopic process of nuclear reactions with the macroscopic energy production in nuclear power systems.

Unit Conversions

Unit conversion is an essential mathematical tool used across physics and engineering to ensure that quantities are expressed in consistent and practical units. This includes converting between energy units (e.g., joules to gigawatts), mass flow rates (e.g., kilograms per second to kilograms per hour), and volumetric flow rates, which is critical for accurate calculations in real-world applications.

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