Question

In the deep space between galaxies, the density of atoms is as low as 10⁶ atoms/m³, and the temperature is a frigid 2.7 K. What is the pressure?

a. 3.7×10⁻¹⁷ Pa
b. 5.2×10⁻¹⁸ Pa
c. 1.8×10⁻¹⁶ Pa
d. 2.3×10⁻¹⁵ Pa

Answer 1

OPTION A.The pressure in the deep space between galaxies with a given density of 10^6 atoms/m^3 and temperature of 2.7 K can be calculated using the ideal gas law, resulting in a pressure of approximately 3.7×10^-17 Pa.

Step-by-step explanation:

The question pertains to finding the pressure in the deep space between galaxies given the density of atoms and temperature. To calculate the pressure, we can use the ideal gas law, which is P = nkT. Here, 'P' is the pressure, 'n' is the number density of particles, 'k' is the Boltzmann constant (1.38×10-23 J/K), and 'T' is the temperature.

Given that the density of atoms is 106 atoms/m3 and the temperature is 2.7 K, we first convert the density of atoms to number density by dividing by Avogadro's number (6.022×1023 atoms/mol) since the ideal gas law uses moles. However, since we're working with a very dilute gas, each atom can be approximated as an independent particle, allowing us to use number density directly in the formula.

Substituting the given values into the ideal gas law, we get:
P = (106)(1.38×10-23 J/K)(2.7 K) = 3.726×10-17 Pa

The pressure in the deep space between galaxies at a density of 106 atoms/m3 and a temperature of 2.7 K is approximately 3.7×10-17 Pa, which corresponding to option a.