4. (a) Derive an integral expression for the probability of a gas molecule of mass m,...

4.

(a) Derive an integral expression for the probability of a gas molecule of mass m, at temperature T is moving faster than a certain speed v_min.

(b) A particle in the atmosphere near the earth’s surface traveling faster than 11 km/s has enough kinetic energy to escape from the earth’s gravitational pull. Therefore, molecules in the upper atmosphere will escape if they do not have collisions on the way out. The temperature of the upper atmosphere is about 1000K. Using the result for (a) and numerical computation to determine the probability that a N₂ molecule at this temperature will escape from the upper atmosphere? Repeat the calculation for a He atom. The escape velocity for the moon is about 2.4 km/s. Explain why the moon has no atmosphere

Expert Solution

Colby Messinger answered 2 years ago

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