   Chapter 10, Problem 47P

Chapter
Section
Textbook Problem

At what temperature would the rms speed of helium atoms equal (a) the escape speed from Earth, 1.12 × 104 m/s and (b) the escape speed from the Moon, 2.37 × 103 m/s? (See Topic 7 for a discussion of escape speed.) Note: The mass of a helium atom is 6.64 × 10−27 kg.

(a)

To determine
The temperature at which rms peed is equal to the escape velocity.

Explanation

Given info: Mass of helium molecule (m) is 6.64×1032kg . The escape velocity from earth ( vrms ) is 1.12×104m/s .

Formula to calculate the temperature at which rms speed is equal to the escape velocity is,

T=mvrms23k

• m is the mass of helium molecule.
• k is the Boltzmann constant.
• vrms is the rms speed which is equal to the escape velocity.

Substitute 6.64×1032kg for m, 1.12×104m/s for vrms and 1

(b)

To determine
The temperature at which rms peed is equal to the escape velocity.

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