First slide

Kinetic theory of ideal gases

Question

At what temperature will the rms speed of oxygen molecule will be sufficient for escaping from the earth?
$(v_{e} = 11.2 k m s^{- 1}, m a s s o f o x y g e n m o l e c u l e = 2.76 \times 10^{- 26} k g a n d k = 1.38 \times 10^{- 23} J k^{- 1})$

Moderate

A

1000 K
B

(B) 2000 K
C

45000 K
D

83600 K

Solution

Let the temperature be T.
According to kinetic theory of gases, translational $K E = \frac{3}{2} k T$
The oxygen molecule will escape from earth if, $\frac{3}{2} k T > \frac{1}{2} m v_{e}^{2}$
i.e., $T > \frac{m v_{e}^{2}}{3 k} o r T > \frac{2.76 \times 10^{- 26} \times {(11.2 \times 10^{3})}^{2}}{3 \times 1.38 \times 10^{- 23}}$
$T > 8.36 \times 10^{4} K$ .

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App