Temperature Estimation for Compressed Air in an Internal Combustion Engine

[cubixguy77]

Homework Statement

In an internal combustion engine, air at atmospheric pressure and a temperature of about 20 degrees C is compressed in the cylinder by a piston to (1/8) of its original volume (compression ratio 8.0).

Estimate the temperature of the compressed air, assuming the pressure reaches 38 atm.

Homework Equations

pv = nRt
$$\Delta$$v = $$\beta$$Vo$$\Delta$$T

$$\beta$$ = .0034 for air

The Attempt at a Solution

If i let p1 * v1 / T1 = p2 * v2 / T2
i can make the associations and end up with T2 = T1 * 38 / 8
however this result is incorrect.
note that i used pv = nRt for this result, I'm not sure if the other equation should be used or not,
i've only gotten garbage answers using it thus far.

Any help would be much appreciated,
Thanks.

 

[ptr]

Try using the other equation you have, though I know not what it is, and then, $$\Delta V = (1-\frac{1}{8}) V_0$$, from which it seems that the original volume is not here required.

-the final temperature is the change in temperature plus the original temperature