Question

dT/dz=−α for z≤11 km

where α=6.5 K/km (Kelvin per km) and z is the height above the sea level. The temperature stays then approximately constant between 11 km and 20 km above sea level.

Assume a temperature of 5 ∘C and a pressure of 1 atm at sea level (1 atm = 1.01325 ×105 N/m^2). Furthermore, take the molecular weight of the air to be (approximately) 29 g/mol. The universal gas constant is R=8.314 JK−1mol−1 and the acceleration due to gravity is g=10 m/s2 (independent of altitude). Assume that air can be treated as an ideal gas.

(a) Under the assumptions above, calculate the atmospheric pressure p (in atm) at z= 10 km above sea level for the case of a linear temperature drop.

p=

unanswered
(b) The cruising altitude of a commercial aircraft is about 33'000 ft (or 10 km). Assume that the cabin is pressurized to 0.8 atm at cruising altitude. What is the minimal force Fmin (in Newton) per square meter that the walls have to sustain for the cabin not to burst? Use the atmospheric pressure found in (a).

Fmin=

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(c) We close a plastic bottle full of air inside the cabin when the aircraft is at cruising altitude of z= 10 km. The volume of the bottle is V1, the pressure and temperature inside the cabin are 0.8 atm and T1=27 ∘C, respectively. Assume that at sea level the atmospheric pressure is 1 atm, and the temperature is decreased by 15 Kelvin with respect to the cabin's temperature.

What is the magnitude of the percentage change in volume of the air inside the bottle when it is brought to sea level? (Enter the magnitude of the percentage change in volume in

∣∣∣ΔV/V1∣∣∣×100=

Answer 1

8:01 exam question

Answer 2

not asking for solution, just tips and considering this is an open book exam

Answer 3

The pressure is 0.2526 atm

Answer 4

what about b and c

Answer 5

and if the temperature was 20∘C?

Answer 6

0.3343

Answer 7

no that's my value for 15º

Answer 8

please guys can you tell formula because I have temp. 10 degree C.

Answer 9

Can anyone please explain the logic of the problem, not a solution a hint.

Answer 10

I found two types of formulas for such a problem - the first one is only for the case of isothermal atmosphere, the second one is for this case, in which the temperature is the function of the height - maybe that's why your solutions aren't correct

Answer 11

Can someone tell the formula because I want to calculate by myself?

Answer 12

Can someone teach us how to do b,c?

Answer 13

dT/dh= - ƴ/(ƴ-1) Mg/Nk with ƴ/(ƴ-1) as a constant is what I remember of the temperature as a function of time. Still I can't comprehend entirely the problem.

Answer 14

I think we have to find out ƴ ant then use dp/p= ƴ/(ƴ-1) dT/T

Answer 15

I used this one: p=p0*[T0/(T0+alpha*(h-h0))]^(g*M/(R*alpha))

Answer 16

hey guys can you please tell the method for part a?

Answer 17

Hi MM, what is h and h_0?

Answer 18

sorry, didn't realize - h is z (height)

Answer 19

I used p=p_0*e(-M*g*h/R*T) but its wrong..Any help pls..:(

where I used h=10km=10000m and temp.T= 273+10=283, M=0.029

Answer 20

you cannot use it, because the temperature is not a constant

Answer 21

Hi MM sorry to disturb you, but I just tried according to ur formula and still getting wrong. I used h-h_0= z= 10000m and T_0= 278, alpha=0.0065 and M=0.029 right?

Answer 22

seems to be OK...really do not know where is the problem...

Answer 23

Thank you for your help. I will try it again.

Answer 24

Any hint for b? and c?

Answer 25

asha which was your pressure value at a?

Answer 26

Hi Daoine, My answer is 0.3289 atm, and I have temp. 10 degree c. This time I afraid to check answer because I don't know part b and c too, so I don't have more attempt. Is it right for 10 degree temp?

Answer 27

who has b & c?

Answer 28

WHAT IS THE FORMULA??