Dear student,

For adiabetic expansion we know that - P(V^gamma) = constant.

Now, the data we have are :-

V1 = 1 litre = 1000 cc
V2 = 1190 cc

P1 = 80 cm of Hg
P2 = 60 cm of Hg.

Now,
P1 (V1)^gamma = P2 (V2)^gamma

And therefore :-

P1 / p2 = ( V2 / V1 )^gamma

4/3 = (119/100)^gamma

And now taking natural logarithm, i.e, ln on both sides we get :-

gamma( ln(119/100) ) = ln(4/3)

And on solving this equation we get :-

gamma = 1.653