A diesel engine's piston compress 16cm3rd of fuel air mixture into 1cm3 The pressure changes from a atmosphere to 48 atmospheres if the initial temp. of the gas was 305k What was the final temerature

They tell you both the pressure ratio (P2/P1 = 48) and the volume ratio (V1/V2 = 16), so you don't have to make any assumptions about whether the compression is adiabatic, or what the specific heat ratio (gamma) is. Just use the perfect gas relationship

P V/T = constant
This means that
T2/T1 = (P2/P1)(V2/V1) = 48/16 = 3
T2 = 915 K (before ignition)