How will the pressure of an ideal gas change if, at a constant concentration, the mean square velocity of the molecules increases by 2 times?
Ideal gas pressure:
P = 1/3 m0 * n * V ^ 2, where P is the pressure of an ideal gas, m0 is the mass of a gas particle, n is the concentration of particles, V ^ 2 is the mean square of the molecular velocity (V is the mean square velocity).
Before increasing the RMS speed:
Р1 = 1/3 m0 * n * V1 ^ 2.
After increasing the RMS speed:
P2 = 1/3 m0 * n * V2 ^ 2, by condition. n – const, V2 = 2V1.
P2 / P1 = (1/3 m0 * n * V2 ^ 2) / (1/3 m0 * n * V1 ^ 2) = V2 ^ 2 / V1 ^ 2 = ((2V1) ^ 2 / V1 ^ 2) = 4V1 ^ 2 / 2V1 ^ 2 = 4.
Answer: The gas pressure will increase by 4 times.
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