Question

The R.M.S. speed of the molecules of a gas of density
4 kg m-3 and pressure 1.2 x 105 Nm-2 is:
(A) 120 ms-1
(B) 300 ms -1
(C) 600 ms-
(D) 900 ms -1​

Answer 1

Answer:

The answer is 300m/s. Check the attached solution.

Explanation:

Answer 2

The R.M.S. speed of the molecules of a gas of density  4 $kg m^{-3}$ and pressure $1.2 \times 10^{5} Nm^{-2}$ is 300 $ms^{-1}$.

Explanation:

It is known that realtion between $V_{r.m.s}$, pressure and mass is as follows.

           $V_{r.m.s} = \sqrt{\frac{3PV}{M}}$

or,                    = $\sqrt{\frac{3P}{\frac{M}{V}}}$ ...... (1)

As it is known that,

                         Density (d) = $\frac{mass}{volume}$ ...... (2)

Therefore, putting the value from equation (2) into equation (1) as follows.

               $V_{r.m.s} = \sqrt{\frac{3P}{\frac{M}{V}}}$  

              $V_{r.m.s} = \sqrt{\frac{3P}{density}$  

                            = $\sqrt{\frac{3 \times 1.2 \times 10^{5} N/m^{2}}{4 kg/m^{3}}$

                             = $3 \times 10^{2} ms^{-1}$

                             = 300 m/s

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