The law of atmospheres states that the number density of molecules in the atmosphere depends on height y above sea level according to where n, is the number density at sea level (where y = 0). The average height of a molecule in the Earth's atmosphere is given by | yn, (1) dy ye D/,T dy avg |n,G) dy eD/A,T dy (a) Prove that this average height is equal to kT/m,g. (b) Evaluate the average height, assuming the temperature is 10.0°C and the molecular mass is 28.9 u, both uniform throughout the atmosphere.

The law of atmospheres states that the number density of molecules in the atmosphere depends on height y above sea level according to where n, is the number density at sea level (where y = 0). The average height of a molecule in the Earth's atmosphere is given by | yn, (1) dy ye D/,T dy avg |n,G) dy eD/A,T dy (a) Prove that this average height is equal to kT/m,g. (b) Evaluate the average height, assuming the temperature is 10.0°C and the molecular mass is 28.9 u, both uniform throughout the atmosphere.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: Determine and zv?> Jor Proo (r,t)

A: The wave function of the second excited state of the hydrogen atom is ψ200=132πro32-rroe-r2ro where…

Q: The atmospheric pressure P(x) (measured in inches of mercury) at height x miles above sea level…

A: Given: The atmospheric pressure (P(x)) above the sea level satisfies the differential equation…

Q: Given the average heart rate of a human is 7.00 beats per minute and the average volume flow of…

Q: (a) Let s(t) be the amount of salt in the tank at time t. Find a differential equation governing…

Q: In a water tank there are four taps, the first one adds water at 5 L/s the second at 6t L/s; the…

A: Given: The rate at which the first tap fills water, R1= 5 L/s. The rate at which the second tap…

Q: f(o)= KBT Vc 1 |--ømø + (1 − 6) ln(1 − 6) + x6(1 − ø) N Π II = kBT [ф Vc N X In(1 - 6) - 6- x6² -…

A: The objective of the question is to derive equation (2.63) using the Flory-Huggins free energy of…

Q: A study room has dimensions of 8 m by 10 m and 3.5 m tall. The air in the room is to be exchanged 7…

A: Given: dimension of room: 8 m × 10 m × 3.5 m velocity of air, v = 8.3 m/s time taken to remove air 7…

Q: (1) A typical bacterium has a mass of 1 picogram (1 × 10-¹2 gram). Calculate the mass of a mole (or…

A: Mass of bacterium m= 10^-12gm.

Q: An oil circulates through a pipe (SG = 0.85), if the speed of the oil is 20 m / s and the diameter…

A: Volumetric flow is speed of oil multiplied by cross sectional area of pipe. Velocity =20m/s Diameter…

Q: т mi is found to be 14 at a speed of 88. What is the expected fuel economy at a gal hr speed of 58mi…

Q: A U.S. 1-cent coin (a penny) has a diameter of 19 mmmm and a thickness of 1.5 mmmm. Assume the coin…

A: diameter of coin= 19 mm Radius of coin (r) = 9.5 mm Thickness (t) of coin = 1.5 mm density of pure…

Q: H'(0) = H"(0) =

Q: A rod of length 24.00 cm has linear density (mass per length) given by λ = 50.0 + 24.5x where x is…

A: length, L=24 cmλ=50+24.5x

Q: Physicians use a machine called a spirometer to measure the maximum amount of air a person can…

A: In this question we are given that physicians use a machine called a spirometer to measure the…

Q: A uniform density sheet of metal is cut into the shape of an isosceles triangle, which is oriented…

A: Consider the whole triangle and the small inner triangle with the slice as the base. These are…

Q: (a) Define the function C(t) = M(t)e – é, teR Show that C(t) = M'(t)e' + M(t)e – é (b) Use (a) and…

A: Given quantities: C(t) = M(t)et - et…

Q: (a) What is the volume (in km3) of Avogadro’s number of sand grains if each grain is a cube and has…

A: The side of the sand grain, l=1 mm=1×10-3 m The width of the beach, b=100 m The depth of the…

Q: Derive the relation between the density of air at STP and the density of air in a laboratory: ρs= ρL…

A: Given : Derive the relation between the density of air at STP and the density of air in a…

Question

The law of atmospheres states that the number density of
molecules in the atmosphere depends on height y above sea
level according to
where n, is the number density at sea level (where y = 0).
The average height of a molecule in the Earth's atmosphere
is given by
| yn, (1) dy
ye D/,T dy
avg
|n,G) dy
eD/A,T dy
(a) Prove that this average height is equal to kT/m,g. (b)
Evaluate the average height, assuming the temperature
is 10.0°C and the molecular mass is 28.9 u, both uniform
throughout the atmosphere.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Trending now

This is a popular solution!

Step by step

Solved in 7 steps with 9 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

T The total surface area, A, of the cylinder can be expressed as A = (a) Find the value of k. (b) Find the value of that makes the total surface area a minimum
There is relatively little space between atoms in solids and liquids, so that the average density of an atom is about the same as matter on a macroscopic scale - approximately 10^3 kg/m^3. The nucleus of an atom has a radius of about 10^-5m of that of the entire atom, and conatins nearly all mass of the atom. a) What is the approximate density, in kilograms per cubic meter, of a nucleus. b) One possible remnant of a supernova, called a neutron star, can have the density of a nucleus, while being the size of a small city. What would be the raduis, in kilometers, of the neutron star with a mass 10 times that of the Sun? The radius of the Sun is 7*10^8 m and its mass is 1.99*10^30 kg
The Ekman number, Ek, arises in geophysical fluid dynamics. It is dimensionless parameter combining seawater density ρ, a characteristic length L, Seawater viscosity μ, and the Coriolis frequency Ωsinφ, where Ω is the rotation rate of the earth and φ is the latitude angle. Determine the correct form of Ek if the viscosity is in the numerator.
Although human lung capacity is about 3 liters per lung, the tidal volume, representing the amount of air that is breathed in and out with each breath is much -3 less, typically about 250 cm7 per lung. The cycle of inhalation and exhalation during normal activity can be represented as a sine curve, as shown in the figure below, where the amount of air in each lung before inhalation begins is about 1.09 liters (the functional residual capacity of the lung) and the time on the horizontal axis has been calculated with the average adult breathing rate of 16 breaths per minute. Volume of air in lungs (L) 1.34 1.09 mm minimum height maximum height 15 We can model each lung as a cylinder of radius 5.95 cm in which one end cap is free to move up and down, increasing and decreasing the volume of the model lung during the breathing process. (a) Using the data above, calculate the minimum and maximum heights (in cm) of the model lung during the breathing process. (Round your answers to at least…
Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 3.663 g, is pressed into a leaf of 2.187 um thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.200 um, what is the length of the fiber? (a) Number i 1.429 Units m^2 (b) Number 72.56 Units
A relationship is found between the number density of cars on a freeway during rush hour, N, and distance. The relationship can be written as k a'N No dr? From this you can conclude that O w = V No O v = No No O v =