Problem 18.54 At the surface of Venus the average temperature is a balmy 460 C d

Question

Problem 18.54

At the surface of Venus the average temperature is a balmy 460 C due to the greenhouse effect (global warming!), the pressure is 92 Earth-atmospheres, and the acceleration due to gravity is 0.894 gEarth. The atmosphere is nearly all CO2(molar mass 44.0g/mol) and the temperature remains remarkably constant. We shall assume that the temperature does not change at all with altitude.

Part A

What is the atmospheric pressure 1.50 km above the surface of Venus? Express your answer in Earth-atmospheres.

Express your answer using two significant figures.

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Part B

What is the atmospheric pressure 1.50 km above the surface of Venus? Express your answer in Venus-atmospheres.

Express your answer using two significant figures.

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Part C

What is the root-mean-square speed of the CO2 molecules at the surface of Venus and at an altitude of 1.50 km ?

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Explanation / Answer

Using the Barometric formula Ph = Po e -Mgh/RT

where g is the acceleration due to gravity, h is the altitude, R is the universal gas constant, T is the temperature and M is the molar mass.

So, if the gravity here is g' = 0.894 g = 0.894 x 9.81 = 8.77 m/s2

h = 1.5 km = 1500 m , M = 44 g /mol = 0.044 kg/mol , T = 460 celcius = 460 + 273 = 733 K

e-Mgh/RT = e-0.044 x 8.77 x 1500/ (8.314 x 733)  = e-0.094979424  = 0.909391645

a.) Po = 92 Earth atm

So, Ph = 92 x 0.909391645 = 83.66403 Earth atm ~ 84 Earth atm

b.) Po = 1 Venus atm

Ph = 1 x 0.909391645 = 0.909391645 Venus atm ~ 0.91 Venus atm

c.) vrms = (3RT/M)1/2 = (3 x 8.314 x 733/ 0.044)1/2  = 644.6 m/s

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