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