How does the average velocity or the root mean square velocity of gas molecules depend on temperature and pressure?

Explanation

The average kinetic energy `(overline(c))` and the root mean square velocity `(c_(rms))` of gas molecules are given by `overline(c)=sqrt((8RT)/(M))`
and `c_(rms)=sqrt((3RT)/(M))`
So, for a given gas `overline(c) prop sqrt(T) and c_(rms) propsqrt(T)` i.e., average velocity or root mean square velocity of the molecules of a given gas is directly proportional to the square root of absolute temperature of the gas.
For 1 mole of an ideas gas `PV=nRT`
Therefore, `overline(c)=sqrt((8RV)/(M)) and c_(rms)=sqrt((3PV)/(M))`
It seems from these two relations that `overline(c)` or `c_(rms)` depends on pressure of the gas. actually they do not. this is because at a given temperature, the value of PV is always constant irrespective of the value of the pressure.