Correct Answer - Option 4 : 1 : 1
CONCEPT:
Root mean square velocity of the gas
- Root mean square velocity (RMS value)is the square root of the mean of squares of the velocity of individual gas molecules.
- It is given as,
\(⇒ v_{rms}=\sqrt{\frac{3RT}{M}}\)
Where vrms= Root-mean-square velocity, M = Molar mass of the gas (Kg/mole), R= Molar gas constant and T = Temperature in Kelvin
CALCULATION:
- Since the same gas is filled in two containers of the same volume, same temperature, and with the pressure of ratio 1 : 2.
Given M1 = M2 = M, V1 = V2 = V, T1 = T2 = T and \(\frac{P_{1}}{P_{2}}=\frac{1}{2}\)
- The rms speed of the gas is given as,
\(⇒ v_{rms}=\sqrt{\frac{3RT}{M}}\) -----(1)
- The rms speed for container 1 is given as,
\(⇒ v_{rms1}=\sqrt{\frac{3RT}{M}}\) -----(2)
- The rms speed for container 2 is given as,
\(\Rightarrow v_{rms2}=\sqrt{\frac{3RT}{M}}\) -----(3)
By equation 2 and equation 3,
\(\Rightarrow\frac{v_{rms1}}{v_{rms2}}=\frac{1}{1}\)
Hence, option 4 is correct.