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Concepts Of Physics MCQ Edition [Volume 2]PhysicsKinetic Theory of Gases

In an experiment, an ideal gas is observed to obey an additional law pV^2 = constant . The gas is initially at a volume V and temperature T . Determine its temperature when it expands to a volume 2V .

Options

  1. AT 2
  2. BT 4
  3. C4T
  4. D2T

Correct answer

A. T 2

Step-by-step solution

For an ideal gas, the equation of state is pV = nRT , which gives p = nRT V . Given the process follows the law pV^2 = constant . Substituting the expression for p into the given law: ( nRT V )V^2 = constant TV = constant This implies T₁ V₁ = T₂ V₂ . Given T₁ = T , V₁ = V , and V₂ = 2V : T V = T₂ (2V) T₂ = T 2

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