Physics, asked by diya20072, 3 months ago

9. What would be the height of the atmosphere if the air density is uniform? Assume that at sea level the air pressure is 10 1300 p a and the air density is 1.3 kg per metre cube​


diya20072: plz answer fast

Answers

Answered by rahulmichael78
0

Explanation:

(a)We use the expression for the variation of pressure with height in an incompressible fluid: p

2

=p

1

−ρg(y

2

−y1.

We take y

1

to be at the surface of Earth, where the pressure is p

1

=1.01×10

5

Pa, and y

2

to be at the top of the atmosphere, where the pressure is p

2

=0. For this calculation, we take the density to be uniformly 1.3kg/m

3

. Then, y

2

−y

1

=

ρg

p

1

=

(1.3kg/m

3

)(9.8m/s

2

)

1.01×10

5

Pa

=7.9×10

3

m=7.9km.

(b)Let h be the height of the atmosphere. Now, since the density varies with altitude, we integrate p

2

=p

1

−∫

0

h

ρgdy.

Assuming ρ=ρ

(1−y/h), where ρ

is the density at Earth's surface and g=9.8m/s

2

for 0≤y≤h, the integral becomes

p

2

=p

1

−∫

0

h

ρ

g(1−

h

y

)dy=p

1

2

1

ρ

gh.

Since p

2

=0, this implies h=

ρ

g

2p

1

=

2(1.01×10

5

Pa)

=16×10

3

m=16km

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