Earth’s atmosphere becomes more rarefied at higher elevations. One way to quantify this is to use the number density of air particles nV , to wit, the number of particles per unit volume. Take the number density at sea level to be n0. 

(a) Calculate how this number density varies with increasing altitude y, measured from sea level. For simplicity, consider the atmosphere to be at a single uniform temperature T. 

Hint: Analyze a parcel of air at an arbitrary height. What’s it doing? What condition therefore applies? 

(b) What fraction of the value at sea level is the number density near the top of the troposphere, at about an altitude of 11.0 km? 

(c) Determine the average height of an “air particle.” 

Hint: The result from (a) can be thought of as a distribution function. How can these functions yield (weighted) averages? Refer to Appendix B as necessary. 

(d) What is the value for this average height for an atmospheric temperature of 10.0 ◦C. Recall that the effective molar mass for air is 28.9 u.