In a diesel engine, the piston compresses the air-fuel mixture from an initial volume of 630 cm^3 to a final volume of 30cm^3. If the initial temperature of the air-fuel mixture is 45 degrees C and the process is occurring adiabatically, determine the final temperature. Comment on the significance of the result.
V(initial) = 6.3x10^-4 m^3
V(final = 3.0x10^-5 m^3
T(initial) = 318.15 K
T(final) = ?
y = 1.4
T(final) = T(initial)*(V(initial)/V(final))^y-1
The Attempt at a Solution
T(final) = 318.15(6.3x10^-4/3.0x10^-5)^0.4
T(final) = 1075.28 K or 802.13 degrees C
Is that on the right track? I found the equation online but I am a little confused how the equation is actually formed from T(f) = P(f)*V(f) / nR which I have in my textbook.