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

A cylindrical tube of cross-sectional area A is fitted with two frictionless pistons. A metallic wire connects the pistons to each other. Initially, the gas temperature is T₀ and its pressure is p₀ , which is equal to the atmospheric pressure. Determine the tension in the wire if the temperature is increased to 2T₀ .

Options

  1. Ap₀ A
  2. Bp₀ A 2
  3. C2p₀ A
  4. D0

Correct answer

A. p₀ A

Step-by-step solution

Let the initial volume of the gas be V . Initially, the pressure of the gas is p₀ and the temperature is T₀ . When the temperature is increased to 2T₀ , the gas tends to expand. However, the pistons are connected by a metallic wire which becomes taut and restricts any further separation of the pistons. Assuming the thermal expansion of the wire is negligible, the volume of the gas remains constant. Using the ideal gas law at constant volume ( V₁ = V₂ ): P₁ T₁ = P₂ T₂ Substituting the given values: p₀ T₀ = P₂ 2T₀ P₂

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