The concentration of gas molecules in the vessel has decreased by 2 times, and the average square of the molecular velocity

The concentration of gas molecules in the vessel has decreased by 2 times, and the average square of the molecular velocity has increased by 4 times. Has the gas pressure changed?

The basic equation of the molecular kinetic theory of gas:
P = (1/3) * m0 * n * v², where m0 is the mass of one gas molecule, n is the gas concentration, v is the average velocity of the molecule.
Expression to determine the pressure before the change:
P1 = (1/3) * m0 * n1 * v1²
After changing the speed of the molecules:
P2 = (1/3) * m0 * n2 * v2²
By condition: n1 = 2 * n2 = n; v2² = 4v1².
Find the ratio P2 / P1:
P2 / P1 = ((1/3) * m0 * n * v2²) / (1/3) * m0 * n * v1² = n2 * v2² / (n1 * v1²) = n2 * 4v1² / (2 * n2 * v1² ) = 4/2 = 2
Answer: the pressure has doubled.



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