Question 935: Thermodynamics & KTG

Question

At what temperature will the rms speed of
oxygen molecules become just sufficient for
escaping from the Earth’s atmosphere?
(Given :
Mass of oxygen molecule (m) = 2.76 × 10
–26
kg,
Boltzmann’s constant k
B
= 1.38 × 10
–23
J K
–1
)

Accepted Answer

Escape velocity from the EarthÃ¢ÂÂs surface is
vescape = 11200 m s
Ã¢ÂÂ1
Let at temperature T, rms speed of oxygen
molecules become just sufficient for escaping
from the EarthÃ¢ÂÂs atmosphere.
Also, V
rms
= V
escape
= $$\sqrt {{{3{k_B}T} \over {{m_{{O_2}}}}}} $$
$$ \Rightarrow $$ 11200 = $$\sqrt {{{3 	imes 1.38 	imes {{10}^{ - 23}} 	imes T} \over {2.76 	imes {{10}^{ - 26}}}}} $$
$$ \Rightarrow $$ T = 8.360 ÃÂ 10
4
K

Answer

2.508 × 10
4
K

Answer

8.360 × 10
4
K

Answer

5.016 × 10
4
K

Answer

1.254 × 10
4
K

Thermodynamics & KTG

At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth’s atmosphere? (Given : Mass of oxygen molecule (m) = 2.76 × 10 –26 kg, Boltzmann’s constant k B = 1.38 × 10 –23 J K –1 )

Choose the correct answer: