Question

Calculate the temperatures at which the root mean square velocity, average velocity and most probable velocity of oxygen gas are all equal to 1500 $m{s}^{-1}$:

• A. $T_{RMS}=2886K,T_{av}=3399K,T_{mp}=4330K$
• B. $T_{RMS}=3399K,T_{av}=2886K,T_{mp}=4330K$
• C. $T_{RMS}=3399K,T_{av}=4330K,T_{mp}=2886K$
• D. None of these

Answer 1

The correct option is A $T_{RMS}=2886K,T_{av}=3399K,T_{mp}=4330K$

(a) THe expression for the RMS speed is $U_{RMS}=\sqrt{\frac{3RT}{M}}$
Substitute values in the above expression.
$1500=\sqrt{\frac{3\times 8.314\times T_{RMS}}{32\times {10}^{-3}}}$
Hence, $T_{RMS}=2886K$
(b) The expression for the average speed is $V_{av}=\sqrt{\frac{8RT}{\pi M}}$
Substitute values in the above expression.
$1500=\sqrt{\frac{8\times 8.314\times T_{av}}{3.1416\times 32\times {10}^{-3}}}$
Hence, $T_{av}=3399K$
(c) The expression for the most probable speed is ${\alpha }_{mp}=\sqrt{\frac{2RT}{M}}$
Substitute values in the above expression.
$1500=\sqrt{\frac{2\times 8.314\times T_{mp}}{32\times {10}^{-3}}}$
Hence, $T_{mp}=4330K$