Q: The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300 K are 6.21 ×10^{-21} J and 484 m/s respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour)

(a)12.42 × 10^{-21} J, 968 m/s

(b)8.78 × 10^{-21} J, 684 m/s

(c)6.21 × 10^{-21} J, 968 m/s

(d)12.42 × 10^{-21} J, 684 m/s

Ans: (d)

Sol: The average translational $\large K.E = \frac{3}{2}kT$

$\large K.E \propto T$

Here temperature becomes doubled, hence K.E also doubled ;

i.e. 12.42 × 10^{-21} J

$\large v_{rms} = \sqrt{\frac{3RT}{M}}$

$\large v_{rms} \propto \sqrt{T}$

Hence , RMS speed becomes √2 times

$\large v’_{rms} = \sqrt{2} \times 484 $

≈ 684 m/s