A sample of ideal gas undergoes isothermal expansion in a reversible manner from volume `V_(1)` to volume `V_(2)`. The initial pressure is `P_(1)` and the final pressure is `P_(2)`. The same sample is then allowed to undergoes reversible expansion under adiabatic conditions from volume `V_(1) to V_(2)`. The initial pressure being same but final pressure is `P_(2)`.
Which relation is correct `(gamma = (C_(P))/(C_(V)))`?

Options

A. `P_(1)V_(1) = P_(2)V_(3)`
B. `P_(2)V_(1) = P_(3)V_(2)`
C. `P_(1)V_(1)^(gamma) = P_(3)V_(2)^(gamma)`
D. `(P_(1))/(P_(2)) = ((V_(2))/(V_(1)))^(gamma-1)`