I got 4V1

a fixed mass of gas at constant pressure occupies a volume.the gas undergoes a rise in temperature so that the Vrms of its molecule is doubled.What is the new volume

Vrms = sqrt( R T/M)

to double Vrms I have to multiply T by 4

P V = n R T
P constant
new T = 4*old T
same P, n , R
so
new V = 4 * old V
so I agree.

To find the new volume, let's start by understanding the relationship between volume and root mean square (rms) velocity. The rms velocity of a gas molecule is related to its temperature according to the following equation:

Vrms = sqrt(3kT / m)

Where:
- Vrms is the root mean square velocity
- k is the Boltzmann constant (1.38 x 10^-23 J/K)
- T is the temperature in Kelvin
- m is the molar mass of the gas in kg/mol

In this question, the pressure and mass of the gas are constant. Since the gas undergoes a rise in temperature that doubles the Vrms, we know that the initial Vrms is multiplied by 2 to get the new Vrms.

So, we can rewrite the equation as follows:

2V1 = sqrt(3kT2 / m)

Now, let's solve for the new volume (V2):

V2 = (sqrt(3kT2 / m)) / 2

Since we're given the initial volume, V1 = 4 (arbitrary units), we can substitute this value into the equation:

V2 = (sqrt(3kT2 / m)) / 2

V2 = (sqrt(3kT2 / m)) / 2
= (sqrt(3kT2)) / 2 * sqrt(m)

Here, we can see that the new volume, V2, will depend on the temperature, T2, and the molar mass of the gas, m. Without knowing these values, we cannot determine the exact new volume.