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Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases

Air ( = 1.4 ) is pumped to a pressure of 2 atm inside a motor tyre at 20^ C . If the tyre suddenly bursts, determine the temperature of the escaping air. Disregard any mixing with the surrounding atmospheric air.

Options

  1. A357 K
  2. B240 K
  3. C386 K
  4. D222 K

Correct answer

B. 240 K

Step-by-step solution

The sudden bursting of a tyre is a fast process, hence it is considered an adiabatic expansion. For an adiabatic process, the relationship between temperature and pressure is given by: T^ P^ 1- = constant T₂ = T₁ ( P₂ P₁ )^ -1 Given: T₁ = 20^ C = 293 K P₁ = 2 atm P₂ = 1 atm (atmospheric pressure) = 1.4 Substituting the values into the equation: T₂ = 293 ( 1 2 )^ 1.4-1 1.4 T₂ = 293 ( 1 2 )^ 0.4 1.4 = 293 ( 0.5 )^ 2 7 Using the approximation (0.5)^ 2 7 0.8203 : T₂ 293 0.8203 240 K

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