Question

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

• A. 12.42 x 10^-21J, 968 m/s.
• B. 6.21 x 10^-21J, 968 m/s
• C. 8.78 x 10^-21J, 684m/s
• D. 12.42 x 10^-21J, 684 m/s

Answer 1

Answer: (D)

12.42 x 10^-21J, 684 m/s

Answer 2

$KE = \frac{3}{2}KT$,
$V_{rms} = \sqrt{\frac{3RT}{M}}$

i.e. $\frac{KE_{2}}{KE_{1}} = \frac{T_{2}}{T_{1}} = 2$

$\therefore$ $KE_{2} = 2KE_{1} = 2x6.21x10^{- 21}$= 12.42 × 10^-21J

$\frac{V_{rms,2}}{V_{rms,1}} = \sqrt{\frac{T_{2}}{T_{1}}}$ = √2

$\therefore$ $V_{rms,2} = \sqrt{2}xV_{rms,1}$
= 684 m/s.

Hence (4) is correct