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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

T

_{1}V

_{1}

^{[tex]\gamma[/tex]-1}=T

_{2}V

_{2}

^{[tex]\gamma[/tex]-1}

Equation 2

P

_{1}V

_{1}

^{[tex]\gamma[/tex]}=P

_{2}V

_{2}

^{[tex]\gamma[/tex]}

## The Attempt at a Solution

Solving Equation 1 for T

^{2}gives:

T

^{2}= T

_{1}(V

_{1}/V

_{2})

^{[tex]\gamma[/tex]-1}

Solving Equation 2 for P

_{2}looks the same, except it is only raised to [tex]\gamma[/tex]

The value for V

_{1}isn't know, but V

_{2}=.09V

_{1}

I substituted this value of V

_{2}into Equation 1, and canceled V

_{1}(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 V

_{1}?