Thermodynamics: Adiabatic Compression

In summary, the conversation was about finding the final temperature and pressure of air being compressed adiabatically in the engine of a Ferrari F355 F1 sports car. The equations used were T1V1^(γ-1)=T2V2^(γ-1) and P1V1^γ=P2V2^γ. The solution involved setting V1 to 1 and using the compression ratio of V2=0.09V1 to find the final temperature in Kelvin.
  • #1
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Homework Statement



The engine of a Ferrari F355 F1 sports car takes in air at 20.0 *C and 1.00 atm and compresses it adiabatically to 0.0900 times the original volume. The air may be treated as an ideal gas with [tex]\gamma[/tex] = 1.40.

Find Final Temp and Final Pressure


Homework Equations



Equation 1
T1V1[tex]\gamma[/tex]-1=T2V2[tex]\gamma[/tex]-1

Equation 2
P1V1[tex]\gamma[/tex]=P2V2[tex]\gamma[/tex]


The Attempt at a Solution



Solving Equation 1 for T2 gives:
T2= T1(V1/V2)[tex]\gamma[/tex]-1

Solving Equation 2 for P2 looks the same, except it is only raised to [tex]\gamma[/tex]

The value for V1 isn't know, but V2=.09V1

I substituted this value of V2 into Equation 1, and canceled V1 (because it was divided by itself), and got the answer of 54.4. This number is way too low, because this is an engine we're talking about.

I'm not sue how to continue the problem. Do I need to take a square root (or I guess in this case the "gamma root"), to cancel out the gamma exponent, and solved for V1?
 
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  • #2
You know:

V1 and V2 as you know the compression ratio from V2 = 0.09 V1. The actual values don't matter, its only the ratio that does. So you can set V1 to 1.

From this you can find T directly.

Hint:

What temperature scale are you meant to be using?
 
  • #3
It's supposed to be in Kelvin? I feel dumb now.

I got them both. Thank you for your help.
 

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