Use p(v)^{gamma}=constant and substitute p=(nrt)/v where gamma=1+2/f

according to adiabatic expansion,

PV^gamma = constant

using ideal gas equatio the above law can be reduced to

TV^gamma-1 = constant

now, applying the given conditions

T V^gamma-1 = T/2 [4 2^1/2 V]^gamma-1

this implies 2 = [2^5/2]^gamma-1

i.e. 2^1 = 2^(5/2(gamma-1))

this impies 1 = 5/2 (gamma-1)

on solving we get,

gamma = 7/5

equating gamma with 1+2/f, where f is the degree of freedom,

we get f = 5