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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 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?

Options

  1. AT₁ T₂ = V₁ V₂
  2. BT₁ T₂ = ( V₁ V₂ )^2
  3. CT₁ T₂ = V₂ V₁
  4. DT₁ T₂ = ( V₂ V₁ )^2

Correct answer

C. T₁ T₂ = V₂ V₁

Step-by-step solution

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 T₁ V₁ = T₂ V₂ . Rearranging the terms, we get: T₁ T₂ = V₂ V₁ Answer: T₁ T₂ = V₂ V₁

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