c. If the pressure P of the rocket's gas at an altitude z, temperature T is decaying at a rate proportional to the current pressure. For the given data derive an expression of the pressure as a function of altitude. Explain why you used the positive or negative sign in your derived expression. i. Evaluate P at z= 5000 m. If the proportional constant = find the value of T used to produce the data if g=9.81 m/s², R=287 J/(kgK). Find the rate of change of P with respect to T @T=200K. ii. RT ii. Altitude (z) Pressure (kP) 500 18.362 1000 16.858 1500 15.477 2000 14.210 2500 13.046 3000 11.977
c. If the pressure P of the rocket's gas at an altitude z, temperature T is decaying at a rate proportional to the current pressure. For the given data derive an expression of the pressure as a function of altitude. Explain why you used the positive or negative sign in your derived expression. i. Evaluate P at z= 5000 m. If the proportional constant = find the value of T used to produce the data if g=9.81 m/s², R=287 J/(kgK). Find the rate of change of P with respect to T @T=200K. ii. RT ii. Altitude (z) Pressure (kP) 500 18.362 1000 16.858 1500 15.477 2000 14.210 2500 13.046 3000 11.977
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:c. If the pressure P of the rocket's gas at an altitude z, temperature T
is decaying at a rate proportional to the current pressure. For the
given data derive an expression of the pressure as a function of
altitude. Explain why you used the positive or negative sign in your
derived expression.
i.
Evaluate P at z= 5000 m.
ii.
If the proportional constant =
find the value of T used to
RT
produce the data if g=9.81 m/s², R=287 J/(kgK).
iii.
Find the rate of change of P with respect to T @T=200K.
Altitude (z)
Pressure (kP)
500
18.362
1000
16.858
1500
15.477
2000
14.210
2500
13.046
3000
11.977
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