A sample of an ideal gas is slowly compressed to onehalf its

A sample of an ideal gas is slowly compressed to one-half its original volume with no change in pressure. If the original root-mean-square speed (thermal speed) of the gas molecules was V, the new speed is squareroot 2V V1 squareroot 2 2 V V/2 V.

Solution

We know that for a fixed pressure, the volume of the gas is directly proportional to the temperature.

That is, for the given compression to half of the initial volume, the temperature would also become half of the initial temperature.

Further, we also know that the root mean squared speed of the gas is given as: Vrms = sqrt(3RT/M)

Now, the new temperature is T(initial)/2

Therefore Vrms = Vrms(initial) / sqrt2 .

Hence, option two of the choices given is the correct one.