Consider a sample of an ideal gas kept in a pouch of some volume. This pouch is then kept in a bigger container of volume V. As soon as we open the pouch then the gas will expand irreversibly in the container. Also consider that this expansion is adiabatic in nature and no energy flows in or out of the container. If we let the system be kept isolated for a sufficient amount of time in which it approximately achieves steady state, then can we say that in this steady state condition every molecule in the gas sample will approximately have the same speed? I thought that the entropy of the system would be maximum in this configuration as the energy is tending to be spread out equally among all molecules. Is this notion of entropy being a measure of the distribution of energy logically correct? Also if it is not correct then is there any mathematical way to find the distribution of the molecular speed of the gas sample?
1 Answer
If we let the system be kept isolated for a sufficient amount of time in which it approximately achieves steady state, then can we say that in this steady state condition every molecule in the gas sample will approximately have the same speed?
No.
We can say that the average speed (average molecular translational kinetic energy) of all the molecules will be the same.
Even before the expansion the speed of every molecule is not approximately the same. They vary about the average of the collection of molecules according to the Maxwell-Boltzmann Distribution. Moreover, the average molecular kinetic energy will be the same after the irreversible expansion as before the expansion. That's because there is no change in internal energy of the gas (system is isolated). For an ideal gas, internal energy is a function of temperature only and temperature is a measure of the average translational KE of the ideal gas molecules.
Hope this helps.
