In the space between two stars,the temperature of a gas cloud is 12 K;and the density of the gas is 1.2 × 10^-⁸ atom/m³.What is the absolute pressure of the gas?

Question

Quizplus · Accepted Answer

The absolute pressure of a gas can be calculated using the ideal gas law, $P = \frac{nRT}{V}$, where $P$ is the pressure, $n$ is the number of moles, $R$ is the ideal gas constant, and $T$ is the temperature in Kelvin. However, given the density and temperature, we can also use $P = nkT$, where $n$ is the number density of particles, $k$ is the Boltzmann constant, and $T$ is the temperature in Kelvin. Given the density of $1.2 \times 10^{8}$ atoms/m³ and a temperature of 12 K, and knowing that $k = 1.38 \times 10^{-23}$ J/K, the pressure $P$ can be calculated as $P = (1.2 \times 10^{8} \text{ atoms/m}^3) \times (1.38 \times 10^{-23} \text{ J/K}) \times 12 \text{ K}$, which gives a result close to the value in option A, $2.0 \times 10^{-13}$ Pa, after converting units and considering the context of the question.

In the Space Between Two Stars,the Temperature of a Gas