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zheka24 [161]
3 years ago
8

The escape velocity on earth is 11.2 km/s. What fraction of the escape velocity is the rms speed of H2 at a temperature of 31.0

degrees Celsius on the earth? Note that virtually all the molecules will have escaped the earth's atmosphere if this fraction exceeds 0.15.
Physics
1 answer:
Sveta_85 [38]3 years ago
7 0

To solve this problem it is necessary to apply the concept related to root mean square velocity, which can be expressed as

v_{rms} = \sqrt{\frac{3RT}{n}}

Where,

T = Temperature

R = Gas ideal constant

n = Number of moles in grams.

Our values are given as

v_e =11.2km/s = 11200m/s

The temperature is

T = 30\°C = 30+273 = 303K

Therefore the root mean square velocity would be

v_{rms} = \sqrt{\frac{3(8.314)(303)}{0.002}}

v_{rms} = 1943.9m/s

The fraction of velocity then can be calculated between the escape velocity and the root mean square velocity

\alpha = \frac{v_{rms}}{v_e}

\alpha = \frac{1943.9}{11200}

\alpha = 0.1736

Therefore the fraction of the scape velocity on the earth for molecula hydrogen is 0.1736

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