Question

At what temp will the rms velocity of oxygen be one and half times of its value at ntp

Answer 1

The correct answer to the question is 660.375 K

CALCULATION:

Let us consider a gas whose molecular mass  is M.

The rms velocity of that gas at any temperature is calculated -

                          rms velocity = $\sqrt{\frac{3kT}{M}}$

Here, k stands for Boltzmann's constant and T is the temperature of the gas in kelvin.

At NTP, the temperature T = 293.5 K.

Hence, the rms velocity of the oxygen at NTP is $\sqrt{\frac{3\times k\times 293.5}{M}$

Let the temperature of oxygen gas is T' where the rms velocity is one and half of its value at NTP.

The rms velocity of oxygen at T' = $\sqrt{\frac{3kT'}{M}$

As per our question, $\sqrt{\frac{3kT'}{M}}=\ \frac{3}{2}\sqrt{\frac{3k\times 293.5}{M}$

                                 ⇒ $\frac{3kT'}{M} =\ \frac{9}{4}\frac{3k\times 293.5}{M}$

                                 ⇒ $T'=\ \frac{9}{4}\times 293.5\ K$

                                 ⇒ $T'=\ 660.375 K$                    [ANS]