In a certain process, the relation between pressure (P) and volume (V), for an ideal gas, is given by PV^2 = \text{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?

  1. A. \frac{T_1}{T_2} = \frac{V_1}{V_2}
  2. B. \frac{T_1}{T_2} = \left(\frac{V_1}{V_2}\right)^2
  3. C. \frac{T_1}{T_2} = \frac{V_2}{V_1} ✓
  4. D. \frac{T_1}{T_2} = \left(\frac{V_2}{V_1}\right)^2

Correct Answer: C. \frac{T_1}{T_2} = \frac{V_2}{V_1}

Explanation

For an ideal gas, P = \frac{nRT}{V}. Substituting this into PV^2 = \text{constant} gives \left(\frac{nRT}{V}\right) V^2 = \text{constant}, which simplifies to TV = \text{constant}. Therefore, T_1 V_1 = T_2 V_2, or \frac{T_1}{T_2} = \frac{V_2}{V_1}.

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