The number density of gas atoms at a certain location in the...

The number density of gas atoms at a certain location in the space above our planet is about $1.00 \times 10^{11} \mathrm{m}^{-3},$ and the pressure is $2.75 \times 10^{-10} \mathrm{N} / \mathrm{m}^{2}$ in this space. What is the temperature there?

Key Concepts

Temperature

Temperature is a measure of the average kinetic energy of the particles in a substance. In gases, a higher temperature corresponds to more rapid particle motion, which in turn increases the pressure if the number density remains constant, as described by the ideal gas law.

Pressure

Pressure is defined as the force exerted per unit area by gas particles colliding with the surfaces of their container. In kinetic theory, it arises from the momentum transfer during these collisions and is directly proportional to the number density of the gas and its temperature.

Boltzmann Constant

The Boltzmann constant 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 microscopic particle dynamics and macroscopic thermodynamic quantities in the ideal gas law.

Ideal Gas Law

The ideal gas law is a fundamental relation in thermodynamics and kinetic theory that connects pressure, volume, temperature, and the amount of gas. It provides the framework for understanding the macroscopic behavior of gases by relating these variables through the equation PV = nRT, or in microscopic terms, p = n k T, where n is the number density and k is the Boltzmann constant.

Number Density

Number density is a measure of the concentration of particles in a given volume. In the context of gaseous systems, it represents the number of molecules or atoms per unit volume and is a key quantity in the ideal gas equation when relating microscopic particle properties to macroscopic phenomena.

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