First slide

Kinetic theory of ideal gases

Question

The average translational energy and the rms speed of molecules of a sample of oxygen gas at 300 K are $6.21 \times 10^{- 21} J$ and 484 ms^-1 respectively. The corresponding values at 600 K are nearly (assuming ideal gas behaviour)

Moderate

A

$12.42 \times 10^{- 21} J, 968 {ms}^{- 1}$
B

$8.78 \times 10^{- 21} J, 684 {ms}^{- 1}$
C

$6.21 \times 10^{- 21} J, 968 {ms}^{- 1}$
D

$12.42 \times 10^{- 21} J, 684 {ms}^{- 1}$

Solution

$E \propto T and v_{rms} \propto \sqrt{T}$ . Hence at 600 K,
$\begin{array}{l} \frac{E_{2}}{E_{1}} = \frac{T_{2}}{T_{1}} \\ \Rightarrow E = 6 .21 \times 10^{- 21} \times \frac{600}{300} \\ = 12 .42 \times 10^{- 21} J \\ and \frac{v_{2}}{v_{1}} = \sqrt{\frac{T_{2}}{T_{1}}} \\ v_{rms} = 484 \times \sqrt{\frac{600}{300}} ≃ 684 {ms}^{- 1} \end{array}$
which is choice (d).

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