Solving Unusual Problems: Using the Polytropic Ideal Gas Equation

AI Thread Summary
The discussion revolves around solving a complex problem using the polytropic ideal gas equation, specifically when cp is constant. Participants clarify the correct formula to use, which is (p2/p1)^(k-1)/k = T2/T1, with k set at 7/5. One user shares their calculations for temperature changes at different pressures, indicating a transition from 1 atm to 1.1 atm yielding 114 degrees and from 1 atm to 0.9 atm yielding 82 degrees. There is a focus on ensuring assumptions are clearly stated and the importance of showing all calculation steps. The conversation highlights the challenges of working with different units, such as Fahrenheit and psi, while confirming the validity of the math presented.
mulgerizze
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Homework Statement
Exhaling air through a mask means the lungs needs to be pressurized to 1.1 atm instead of the normal 1atm. To exhale through the mask the lungs are depressurized to 0.9 atm. In either case the temp of the lungs wont be the normal 98.7 degrees Fahrenheit. What is the temperature swing of the lungs in this case?
Relevant Equations
Entropy, polytropic equation for an ideal gas
My teacher likes to make really weird problems. How can I start this problem? The only thing I thought of doing is using the polytropic ideal gas equation when cp= constant. (p2/p1)^k-1/k = T2/T1 and making p1 and t1 in each case the normal state of the lungs
 
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Hello (again),

And what do you get when you follow your thought ?

##\ ##
 
BvU said:
Hello (again),

And what do you get when you follow your thought ?

##\ ##
I got that the temperature from 1 atm to 1.1 atm was 114 and the temperature from 1 atm to 0.9 atm was 82
 
BvU said:
I suppose you used (p2/p1)^(k-1)/k = T2/T1 and not (p2/p1)^k-1/k = T2/T1
And k = 7/5 ?

I have trouble dealing with units like Fahrenheit and psi, but I suppose your math is ok.

So if your asumptions (did you list them ?) are correct, this is what omes out. Seems a bit hefty to me, but who knows ...

https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/
(don't just dump a number, show your steps)

##\ ##
I assumed cp = constant and that the breathable air is an ideal gas.

My steps for for p=1.1 to p=1 k=1.4 were 98.7+460(1.1atm/1atm)^(1.4-1)/1.4

For p=0.9 to p=1 k=1.4 . 98.7+460(.9atm/1atm)^(1.4-1)/1.4
 
mulgerizze said:
Homework Statement:: To exhale inhale through the mask the lungs are depressurized to 0.9 atm.
Fixed typo for you in your problem statement. :smile:
 
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