In a certain process, the relation between pressure (P) and volume...

The given process equation is $PV^2 = \text{constant}$.

For an ideal gas, the equation of state is $PV = nRT$, which gives $P = \dfrac{nRT}{V}$.

Substituting the expression for $P$ into the process equation:

\left(\dfrac{nRT}{V}\right) V^2 = \text{constant}$<br><br>$T V = \dfrac{\text{constant}}{nR} = \text{constant}$<br><br>This implies that$T_1 V_1 = T_2 V_2$.<br><br>Rearranging the terms, we get:<br><br>$\dfrac{T_1}{T_2} = \dfrac{V_2}{V_1}$<br><br>Answer:$\dfrac{T_1}{T_2} = \dfrac{V_2}{V_1}