2. Mass of Earth\'s Atmosphere (10 pts) There are no new skills required to answ

Question

2. Mass of Earth's Atmosphere (10 pts) There are no new skills required to answer questions like this (and 1b) beyond what we discussed in class at the beginning of the semester: basic manipulation of quantities and their units. (2) Earth's surface pressure is approximately 1 kg per square centimeter. What is Earth's surface pressure in kilograms per square kilometer? (Appendices C.3 and C.4 might be helpful for this) a. b. (2) What is Earth's surface area, in square kilometers, assuming Earth's radius is 6400 km (and using the fact that surface area is given by 4 × × (Radius)"? (2) Using your answers for (a) and (b), what is the total mass of Earth's entire atmosphere, in kilograms? (look at the units!) c. (2) What fraction (or percentage, if you prefer) of Earth's total mass does its atmosphere account for? (Use Appendix E for Earth's mass) d. (2) The Earth's oceans are estimated to have a mass of about 1.4 x 10 l kg. How many times more massive are the Earth's oceans than the Earth's atmosphere? e.

Explanation / Answer

a.

Earth surface pressure= 1kg/cm2

1 kilometer = 1000 meter and 1 meter = 100 centimeter

1 kilometer = 1000 x 100 centimeter or 1 centimeter= 10-5 kilometer

1kg/cm 2 = 1 kg/ (10-5)2kilometer = 1010kilogram/kilometer2

b.

Surface area = 4 x phi x r2

=4 x (22/7) x (6400)2kilometer2

Surface area = 514,925,714.3kilometer2 or 5.149257143x108 square kilometer

c.

Since pressure = (Mass/area)

Mass = pressure x area

Mass = 1010 x 5.149257143x108 kilogram

Mass = 5.149257143x1018 kilogram

d.

Earth crustal radius is 6400 kilometer while for atmosphere is around 440 miles / 700 kilometers. Which is about 1/10th of earth radius or 1/20 of its diameter. Average density of earth material is 5520 kg/m3and for air is 1.225 kg/m3. Therefore, air density is 2.21x10-4 times the density of material from which earth is composed of.

Accounting for depth and density the mass of atmosphere is= 1/20 x 2.21x10-4

Therefore, mass fraction of earth's mass due to atmosphere is 1.10 x 10-5

e.

Times earth oceans are massive = Mass of ocean/ mass of earth

= (1.4 x 1021)kg/(5.149257143x1018)

Therefore,Number of times earth oceans are massive than earth itself

= 271.88 times

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