Physics
Physics
5th Edition
ISBN: 9781260486919
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 9, Problem 82P

(a)

To determine

Find the air pressure difference between the top and bottom of the Willis tower.

(a)

Expert Solution
Check Mark

Answer to Problem 82P

The air pressure difference between the top and bottom of the Willis tower in Pascal is 5.2kPa and in atmospheric condition is 0.051atm.

Explanation of Solution

Write the equation for pressure difference.

ΔP=ρgh (I)

Here, ρ is the density of the air at 20°C, g is the gravitational acceleration, h is the height of the Willis tower, and ΔP is the pressure difference between the top and bottom of the Willis tower.

Conclusion:

Substitute 1.20kg/m3 for ρ, 9.80m/s2 for g, and 440m for h in equation (I).

ΔP=(1.20kg/m3)(9.80m/s2)(440m)=5174.4Pa=5.2×103Pa(103kPa1Pa)5.2kPa

Thus, the pressure difference between the top and bottom of the Willis tower in Pascal is 5.2kPa.

Convert pressure difference in atm.

ΔP=5.2×103Pa(1atm1.013×105Pa)=5.13×102atm=0.051atm

Thus, the pressure difference between the top and bottom of the Willis tower in atmospheric condition is 0.051atm.so it is less at the top of the tower.

(b)

To determine

Find the number of pressure decreases in Pa for every meter of altitude.

(b)

Expert Solution
Check Mark

Answer to Problem 82P

The number of pressure decreases in Pa for every meter of altitude is 11.8Pa/m.

Explanation of Solution

Write the equation for pressure difference.

ΔP=ρgΔy (II)

Here, Δy is the altitude of the tower in which the pressure decreases.

The number of Pa the pressure decreases for every meter of altitude is.

ΔPΔy=ρg (III)

Conclusion:

Substitute 1.20kg/m3 for ρ and 9.80m/s2 for g in equation (III).

ΔPΔy=(1.20kg/m3)(9.80m/s2)=11.76Pa/m11.8Pa/m

Therefore, the number of pressure decreases in Pa for every meter of altitude is 11.8Pa/m.

(c)

To determine

Find the altitude at which the atmospheric pressure reaches zero.

(c)

Expert Solution
Check Mark

Answer to Problem 82P

The altitude at which the atmospheric pressure reaches zero is at 8.61km.

Explanation of Solution

Write the equation for pressure variation with depth.

P2=P1+ρgd (IV)

Here, P2 is the pressure at the surface point 2, d is the depth, and P1 is the pressure at the surface point 1.

If the object is kept on the atmosphere, suppose we take point 1 at the surface and point 2 is a depth, then P1=Patm so the pressure at a depth below the surface equation (IV) can be written as,

P2=Patm+ρgd (V)

Substitute 0 for P2 and h for d in the equation (V) and solve for h.

Patmρgh=0Patm=ρghh=Patmρg

Conclusion:

Substitute 1.20kg/m3 for ρ, 1.013×105Pa for Patm, and 9.80m/s2 for g in above equation.

h=(1.013×105Pa)(1.20kg/m3)(9.80m/s2)=0.0861×105m=8.61×103m(103km1m)=8.61km

Therefore, the altitude at which the atmospheric pressure reaches zero is at 8.61km.

(d)

To determine

Find the true or false statement

(d)

Expert Solution
Check Mark

Answer to Problem 82P

The true statement, if the pressure is non-zero at a certain altitude and the atmosphere extends to a higher altitude.

Explanation of Solution

Since the zero altitude is calculated from an expression inverse proportionality to the air density, so that decreasing air density means that the atmospheric extends to a higher altitude.

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