What is the final translational rms speed of the molecules?

Question

Initially, the translational rms speed of a molecule of an ideal gas is 460 m/s. The pressure and volume of this gas are kept constant, while the number of molecules is increased by a factor of 6.

Answer 1

The key here that you are adding mass to a fixed volume while keeping pressure fixed. Since

pV = nkT where n = number of molecules/m^3, k = Boltzman's constant and T = temperature., the since pV = constant and n is increasing. T must decrease. Then since

1/2mv^2 = 3/2kT --> v = speed of molecule must also decrease.

Now initially pV = n0kT0 = n0*1/2*mv0^2 v0 = 460 m/s

FInal state pV = 6n0kT = 6n0*1/2mv^2 = n0*1/2mv0^2

So v =v0/sqrt(6) = 187.79 m/s

Answer 2

speed is not a factor ,the split ever 1/2 second.or fraction.