The relation between internal energy U, pressure P and volume V  of a gas in an adiabatic process is:U  = a + bPV where a = b = 3. The ratio of specific heats [ γ ] is

For an adiabatic process, dQ=dU+PdV         [dQ=0] or  d[a+bPV]+PdV=0or bP dV + bV dP + P dV = 0 or (b +1)P dV + bV dP = 0or  (b+1)dVV+bdpp=0or (b +1) logV + blog P = constantVb+1Pb=constant or PVb+1b=  constant ∴γ=b+1b=43=1.33