Dear student,

T1 = 10 = 283K

Let initial volume be V1 and final be V2 .

Now, as gas is adiabatically compressed to one third of it's original volume then :

V2 = 1/3 of V1

That is :-

V2 / V1 = 1/3

And, gamma = 1.5

And since the gas is compressed, so we will use

T2 (V2)^(gamma - 1) = T1 (V1)^(gamma - 1)

Therefore it becomes -

T2 = T1 (V1/V2)^(gamma - 1)

T2 = 283 (3)^0.5 = 283√3

Therefore the final temperature is :-

T2 = 490.17K