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

Answered: Image /qna-images/answer/570fdce3-4255-4ca8-b032-a3ead84eca4d.jpg

Answered: The law of atmospheres states that the…

University Physics Volume 2

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Chapter2: The Kinetic Theory Of Gases

Section: Chapter Questions

Problem 52P: The partial pressure of carbon dioxide in the lungs is about 470 Pa when the total pressure in the...

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An important design consideration in two-phase pipe flow of solid-liquid mixtures is the terminal settling velocity below, which the flow becomes unstable and eventually the pipe becomes clogged. On the basis of extended transportation tests, the terminal settling velocity of a solid particle in the rest water given by VL = FL√2gD(S − 1), where FL is an experimental coefficient, g the gravitational acceleration, D the pipe diameter, and S the specific gravity of solid particle. What is the dimension of FL? Is this equation dimensionally homogeneous?
If the density (mass divided by volume) of the wall material is the same as that of pure water, what is the mass (in mgmg) of the cell wall, assuming the cell to be spherical and the wall to be a very thin spherical shell?
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How many cubic meters of helium are required to lift a balloon with a 400-kg payload to a height of 8 000 m? Take He = 0.179 kg/m3. Assume the balloon maintains a constant volume and the density of air decreases with the altitude z according to the expression air = 0ez/8, where z is in meters and 0 = 1.20 kg/m3 is the density of air at sea level.
Check Your Understanding If you consider a very small object, such as a grain of pollen, in a gas, then the number of molecules striking its surface would also be relatively small. Would you expect the grain of pollen to experience any fluctuations in pressure due to statistical fluctuations in the number of gas molecules striking it in a given amount of time?
Show that 3, by calculating the change in volume V of a cube with sides of length L.
The partial pressure of carbon dioxide in the lungs is about 470 Pa when the total pressure in the lungs is 1.0 atm. What percentage of the air molecules in the lungs is carbon dioxide? Compare your result to the percentage of carbon dioxide in the atmosphere, but 0.033%.
Check Your Understanding The recommended daily amount of vitamin B3 or niacin, C6NH5 O2, for women who are not pregnant or nursing, is 14 mg. Find the number of molecule of niacin in that amount.
Assuming the human body is primarily made of water, estimate the number of molecules in it. (Note that water has a molecular mass of 18 g/mol and there are roughly 1024 atoms in a mole)
The gas law for an ideal gas at absolute temperature T(in kelvins), pressure P (in atmospheres), and volume V(in liters) is PV=nRT, where is the number of moles ofthe gas R =0.0821 and is the gas constant. Suppose that,at a certain instant P=8.0, atm and is increasing at a rateof 0.10 atm/min and V=10L and is decreasing at a rateof 0.15 L/min. Find the rate of change of T with respect totime at that instant if n=10 mol.
The gas law for a fixed mass mm of an ideal gas at absolute temperature T, pressure P, and volume V is PV=mRT, where R is the gas constant. Find the partial derivative (∂P/∂V) (∂V/∂T) (∂T/∂P) = ?
If the ideal gas law (PV = kT) is used to find P when T and V are given, but there is an error of 0.3% in measuring T and an error of 0.8% in measuring V, find approximately the greastest percent error in P?

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