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  3. 4. (a) derive an integral expression for the proba

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

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Advance Math

4.

(a) Derive an integral expression for the probability of a gasmolecule of mass m, at temperature T is movingfaster than a certain speed vmin.

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

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