posted by Ana on .
If two molecules have the same temperature does it affect their average velocity depending on how heavy the molecules are or not?
For the same T, the kinetic energy is the same for the two molecules.
K. E. = 1/2 m*v2
So if K. E. is same and the masses are different, what must be true about the velocities of each.
That they are the same?
of course not.
Use K. E. = 1/2 m*v2
Now just put some numbers in. Say K. E. = 10 for both molecules.
Now put in something like 10 for mass for one and calculate v. Then put in 5 for the other and calculate v. Is v the same? No. Can you see that if 1/2 mv^2 = a constant, then if m goes UP, the v must go DOWN; or if m goes DOWN, then v must go UP. If one increases the other must decrease to keep the constant a constant. right?
Think about Boyle's law. It was
PV = k.
If pressure of a gas goes up the volume must go down. If presure goes down the volume goes up. You know that from the gas laws. This is the same kine of thing but instead of PV = k we have k=K.E. = 1/2 mv^2 and we know K. E. is the same from the kinetic moleuclar theory that tells us the K. E. is the same for all molecules at the same temperature.