   Chapter 10, Problem 10CQ

Chapter
Section
Textbook Problem

The air we breathe is largely composed of nitrogen (N2) and oxygen (O2) molecules. The mass of an N2 molecule is less than the mass of an O2 molecule. (a) For air at 300 K, is the average kinetic energy of an N2 molecule greater than, less than, or equal to the average kinetic energy of an O2 molecule? (b) Is the rms speed in air of an N2 molecule greater than, less than, or equal to the rms speed in air of an O2 molecule?

(a)

To determine
The average kinetic energy of nitrogen and oxygen.

Explanation

The average kinetic energy is,

KE=32kT

• k is the Boltzmann constant.
• T is the temperature.

The average kinetic energy is directly proportional to the temperature. Therefore, the ratio of average kinetic energy of nitrogen ( KEN ) and average kinetic energy of oxygen ( KEO ) is equal to the ratio of temperature of nitrogen ( TN ) and temperature of oxygen ( TO ).

KENKEO=TNTO          x

(b)

To determine
The rms speed of nitrogen and oxygen.

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