A very expensive gas is sold by the molecule and the price i

A very expensive gas is sold by the molecule, and the price is proportional to the velocity of individual molecule: price in $=v/ . If I buy a bulb of these gaseous molecules, what is the average price per molecule,and does the price depend on the temperature of the bulb?

Solution

For a gas, the average velocity of the molecules is given by the root mean squared velocity of the gas molecules which is given as: V = sqrt[(3RT) / M] where M is the molar mass of the gas in kilograms per mole

Hence the average price per molecule will be sqrt[(3RT) / M] dollars.

And yes, the velocity is depends on the temperatute of the bulb.