In a certain process, the relation between pressure (P) and volume (V), for an ideal gas, is given by PV2 = constant. If the initial temperature is T1 and the final temperature is T2; and the initial volume is V1 and the final volume is V2, then which one of the following is correct?

For an ideal gas, the state equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the universal gas constant, and T is temperature. From this, we can express pressure as P = nRT/V.

The given process follows the relation PV2 = constant. Substituting the expression for P into this relation:

(nRT/V) × V2 = constant
nRT × V = constant

Since n and R are constants for a given mass of gas, the equation simplifies to T × V = constant. This implies that for initial and final states:

T1V1 = T2V2

Rearranging the terms to find the ratio of temperatures, we get:

T1/T2 = V2/V1

Thus, option C is the correct relationship.