What is the correlation between entropy and velocity distribution?

[lschuh]

Hello,
The Boltzmann velocity distribution may show the curves for a low (T1) and a high (T2) temperature. The T2 curve is broader and flatter. A flatter curve means: a broad range of speed/KE. This means more micro states, which means a higher entropy S. This explains the increase of S with increasing T. Consent?
The transfer of heat Q increases T of an ideal gas, because the KE increases - The velocity v of the particles increases

Is it correct to state the following:
Q is represented by the average (root of v^2) in the Maxwell Boltzmann Distribution curve at T
S is represented by the width of the Maxwell Boltzmann Distribution curve at T

Regards
Lo

 

[Dale]

This explains the increase of S with increasing T. Consent?

A higher temperature has a lower entropy. $$dS=\frac{\delta Q}{T}$$
For the same $\delta Q$ you get a smaller $dS$ for a bigger $T$