A nebula-a region of the galaxy where new stars are...

A nebula-a region of the galaxy where new stars are forming-contains a very tenuous gas with 100 atoms/cm". This gas is heated to $7500 \mathrm{K}$ by ultraviolet radiation from nearby stars. What is the gas pressure in atm?

Key Concepts

Unit Conversion

Unit conversion is vital in ensuring that all physical quantities are expressed in consistent and compatible units. When calculating gas pressure, conversion of number density from atoms per cubic centimeter to atoms per cubic meter, and later converting the resulting pressure into atmospheres, is necessary for an accurate and meaningful result.

Ideal Gas Law

The ideal gas law, often expressed as P = n k T or PV = nRT, provides a fundamental relationship between pressure, volume, temperature, and the number of particles in a gas. It is key to determining the pressure exerted by a gas when its density and temperature are known by relating microscopic particle behavior to macroscopic properties.

Number Density

Number density refers to the number of particles per unit volume. It is a critical parameter in calculating gas properties, as it directly contributes to pressure when multiplied by the thermal energy per particle. This concept is essential for understanding the behavior of extremely low-density gases.

Boltzmann Constant

The Boltzmann constant (k) is a fundamental physical constant that relates the average kinetic energy of particles in a gas to its temperature. It plays a crucial role in the ideal gas equation at the microscopic level, connecting the thermal motion of individual particles to the overall pressure of the gas.

Temperature

Temperature, particularly measured in Kelvin in thermodynamic contexts, reflects the average kinetic energy of the particles in a system. In the ideal gas law, higher temperatures increase the kinetic energy of particles, leading to a higher gas pressure.

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