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

In the morning, at an air temperature of 20^ C , air is pumped into an automobile tyre's tube to a pressure of 200 kPa . Over the course of the day, the temperature increases to 40^ C and the tube expands by 2 % . Determine the pressure of the air in the tube at this new temperature.

Options

  1. A400 kPa
  2. B392 kPa
  3. C214 kPa
  4. D209 kPa

Correct answer

D. 209 kPa

Step-by-step solution

Using the ideal gas equation: P₁ V₁ T₁ = P₂ V₂ T₂ The initial pressure is P₁ = 200 kPa , initial temperature is T₁ = 20^ C = 293 K , and initial volume is V₁ = V . The final temperature is T₂ = 40^ C = 313 K and the final volume is V₂ = V + 0.02V = 1.02V . Substituting the values into the equation: 200 V 293 = P₂ 1.02V 313 P₂ = 200 313 293 1.02 P₂ = 62600 298.86 209.46 kPa The pressure of the air in the tube is approximately 209 kPa .

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