Nuclear fusion, the energy source of the Sun, hydrogen...

Nuclear fusion, the energy source of the Sun, hydrogen bombs, and fusion reactors, occurs much more readily when the average kinetic energy of the atoms is high- that is, at high temperatures. Suppose you want the atoms in your fusion experiment to have average kinetic energies of $6.40 \times 10^{-14} \mathrm{J}$. What temperature is needed?

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Key Concepts

Boltzmann Constant

The Boltzmann constant (denoted as kB) is a fundamental physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. It serves as the bridge between macroscopic and microscopic physics, enabling the conversion of energy quantities expressed in Joules to temperatures measured in Kelvin.

Temperature in Kelvin

Temperature is a measure of the average kinetic energy of particles and, in the context of thermal physics, is most appropriately expressed in Kelvin. Kelvin is the SI unit of temperature, ensuring a consistent and absolute scale for calculations which avoid negative values and are essential in high-energy phenomena such as nuclear fusion.

Kinetic Energy–Temperature Relationship

In thermal physics, the average kinetic energy per particle in a system at thermal equilibrium is directly related to its temperature, typically expressed as (3/2)kBT for a three-dimensional ideal gas. This relationship forms the basis of connecting the microscopic energy of particles to the macroscopic temperature, allowing us to calculate the temperature necessary for a system if the average kinetic energy is known.

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