Find the temperature at which the rms speed of helium ( M = 4 g/mol) equals the escape speed from the Earth, 1.12 × 1 0 4 m/s. Give the answer in units of 1 0 3 K (nearest integer). R = 8.314 J/(mol K).

T = 3 R M v e 2 = 3 × 8.314 0.004 × ( 1.12 × 1 0 4 ) 2 = 20117 K, about 20 × 1 0 3 K.

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Physics - Heat & Thermo Question with Solution | TestHub

PhysicsHeat & ThermoKinetic Theory of Gases and Gas LawsMedium2 minQB

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Find the temperature at which the rms speed of helium ( $M = 4$ g/mol) equals the escape speed from the Earth, $1.12 \times 1 0^{4}$ m/s. Give the answer in units of $1 0^{3}$ K (nearest integer). $R = 8.314$ J/(mol K).

Answer:

20.00

Solution:

$T = \frac{M v _{e}^{2}}{3 R} = \frac{0.004 \times ( 1.12 \times 1 0 ^{4} ) ^{2}}{3 \times 8.314} = 20117$

K, about 20 $\times 1 0^{3}$ K.

Subject:PhysicsTopic:Heat & ThermoSubtopic:Kinetic Theory of Gases and Gas Laws

⏱ 2mℹ️ Source: QB

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