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KVPY2017PhysicsKinetic Theory of Gases

A long cylindrical pipe of radius 20 ~cm is closed atits upper end and has an airtight piston of negligible mass as shown. When a 50 Kg mass is attached to the other end of the pistion, it moves down. If the air in the enclosure is cooled from temperature T to T- T , the piston moves back to its original position. Then T / T is close to (Assuming air to be an ideal gas, g=10 ~m / s ² , atmospheric pressure is 10⁵ Pas

Options

  1. A0.01
  2. B0.02
  3. C0.04
  4. D0.09

Correct answer

C. 0.04

Step-by-step solution

Initially pressure =P₀ When 50 ~kg mass is suspended array l pressure =P₀- m g A (temp = constant ) P₀ V₁= (V₀- m g A ) V_ f (P₀- m g A ) V_ f =n R T (P₀- m g A ) V_ i =n R(T- T) = V_ f V_ i = T T- T T- T T = V_ i V_ f = T T = (P₀- m g A ) 1 P₀ array aligned T T &= mg AP ₀ &= 50 10 3.14 (0.2)² 10⁵ &= 500 12.56 10³ &= 5 125.6 = 1 25 =0.04 aligned

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