In a certain process, the relation between pressure (P) and volume (V), for an ideal gas, is given by PV^2 = constant . If the initial temperature is T_1 and the final temperature is T_2; and the initial volume is V_1 and the final volume is V_2, then which one of the following is correct?
C. T_1 T_2 = V_2 V_1
The given process equation is PV^2 = constant . For an ideal gas, the equation of state is PV = nRT, which gives P = nRT V . Substituting the expression for P into the process equation: ( nRT V ) V^2 = constant T V = constant nR = constant This implies that T_1 V_1 = T_2 V_2. Rearranging the terms, we get: T_1 T_2 = V_2 V_1 Answer: T_1 T_2 = V_2 V_1
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