Thermodynamics: Adiabatic Compression

[Wobble]

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 $$\gamma$$ = 1.40.

Find Final Temp and Final Pressure

Homework Equations

Equation 1
T₁V₁^$$\gamma$$-1=T₂V₂^$$\gamma$$-1

Equation 2
P₁V₁^$$\gamma$$=P₂V₂^$$\gamma$$

The Attempt at a Solution

Solving Equation 1 for T² gives:
T²= T₁(V₁/V₂)^$$\gamma$$-1

Solving Equation 2 for P₂ looks the same, except it is only raised to $$\gamma$$

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?

 

[xxChrisxx]

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?

 

[Wobble]

It's supposed to be in Kelvin? I feel dumb now.

I got them both. Thank you for your help.