engine + reversible adiabatic compression

[cralston]

Hi, I am having a lot of problems!!! I can't figure this problem out:

In a diesel engine the air is heated by reversible adiabatic compression from T1 = 300K, at P1 = 1 atm to T2 = 800K

A) What volume ratio (V2/V1) is required to achiene the final temperature, T2= 800 K? The molar heat capacity of air is Cv= (5/2)R. (Note the inverse ratio V1/V2 is called the compression ratio.

B) What is the pressure when the ignition temperature T2= 800K is reached?

C) What is the change in entropy per mole of the ideal gas when it undergoes this process?

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Here is one of the many different ways that I have tried to solve this problem.
A) I just pluged the initial P1 and T1 into the PV=nRT formula to get the V1. Then I put P1T1=P2T2 to solve for P2, but this can't be right because the volume has to have changed. So I don't know what to do.
B) after I can figure out the volume ratio I can figure out what V2 is then use V2 and T2 to find P2 in PV=nRT.
C)Isn't the change in entropy zero because S= q/T and q is zero because its adiabatic?

PLEASE help, I would really appreciate it. Thanks!