Particle of mass m in a uniform gravitational field

Reference no: EM13307259

Consider a particle of mass m in a uniform gravitational field. Its potential energy is E(h) = mgh,where h is the height above sea level and g is the earth's gravitational constant, g = 9:8 m/s2.

(i) According to the Boltzmann distribution, what is the probability p(h) of finding the particle at
height h, relative to the probability p(0) of finding it at sea level (h = 0), at temperature T?

[In truth, p(h) is a probability density, since h is a continuous variable. A more proper way to word
this question would be in terms of the probability p(h)h of finding the particle in a small range of height between h and h+h. But since (p(h)h)=(p(0)h) = p(h)=p(0), the answer would be the same.]

(ii) Now imagine that there are N such masses, all identical and non-interacting. On average, how many of these objects reside at height h, relative to the number at sea level? Express your answer in terms of relative densities, (h)=(0), where (h) denotes the average number of particles per unit volume at height h.

(iii) Many people (including me) are susceptible to altitude sickness due to oxygen depletion at elevations greater than 10,000 feet above sea level. Using your result from part (ii), estimate the density of molecular oxygen at this elevation, relative to that at sea level. In performing this calculation, assume that the earth's atmosphere has a temperature of 300 K throughout.

Reference no: EM13307259

Questions Cloud

Derermine the velocity and acceleration of point p : At the same instant the frame h, not the horizontal blade, rotates about a vertical axis with a constant angular velocity w=0.9 rad/s, measured relative to h

Why your program should require o(logn) time per order : The double action system operates as follows. When a new buy order of $x arrives it is simply stored for future use if none of the stored sell orders has an asking price lower than or equal to $x.

Determine the time it takes for the light to strike ground : Falling light. According to general relativity and the equivalence principle, light is bent by gravity. Determine the time it takes for the light to strike the ground

What was the initial concentration of cocl2 : What was the initial concentration of COCl2?

Particle of mass m in a uniform gravitational field : Consider a particle of mass m in a uniform gravitational field. Its potential energy is E(h) = mgh,where h is the height above sea level and g is the earth's gravitational constant, g = 9:8 m/s2.

Determine the distance that a particle on the rim moves : The flywheel of a prototype car engine is under test. The angular position of the flywheel is given by x = (3.0rad/s3)t3 and the diameter of the flywheel is 36cm.

Competencies between nurses prepared : Write a formal paper discussing the differences in competencies between nurses prepared at the associate-degree level versus the baccalaureate-degree level in nursing.

Compute the fraction of time mary spends using her telephone : Assuming a single-server limited-capacity Bernoulli queuing process with 1-minute frames, compute the fraction of time Mary spends using her telephone.

Long cylindrical glass tube : A 10.0cm long cylindrical glass tube, sealed at one end, is filled with ethanol. The mass of ethanol needed to fill the tube is found to be 11.48g . The density of ethanol is 0.789 g/mL.

User Account

All Pages