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A sound wave passing through the air at NTP produces a pressure of 0 . 001 dyne cm - 2 during a compression. The corresponding change in temperature (given γ = 1.5 and assume gas to be ideal) is

Options

  1. A8 . 97 × 10 - 4   K
  2. B9 . 87 × 10 - 6 K
  3. C8 . 97 × 10 - 8 K
  4. D9 . 87 × 10 - 4 K

Correct answer

C. 8 . 97 × 10 - 8 K

Step-by-step solution

T γ P 1 - γ = constant Differentiating γ T γ - 1 dT P 1 - γ + T γ 1 - γ P - γ dP = 0 or, dT = γ - 1 T γ P dP or, dT = 1.5 - 1 1.5 2 7 3 7 6 × 13.6 × 9 8 1 × 0.001 ⇒ 8 . 97 × 10 - 8   K

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