Say I have an ideal gas that has a known $P_1$, $P_2$, $T_1$, and $T_2$ undergoing a reversible adiabatic process. I want to find the work done so I must use $PV = RT$ to get the change in $V$, so that's $$\frac {P_1V_1}{T_1} = \frac {P_2V_2}{T_2}$$, and also $$W = \int PdV = P(V_2 - V_1)$$.
My problem is, these are only 2 equations and 3 unknowns. How do I solve $V_1$, $V_2$, and $W$? Also, in the second equation, is the value of $P$ equal to $P_1$ or $P_2$?