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An ideal diatomic gas with C v = 5 R 2 occupies a volume V 1 at a pressure P 1 . The gas undergoes a process in which the pressure is proportional to the volume. At the end of process the rms speed of the gas molecules has doubled from its initial value then the heat supplied to the gas in the given process is

Options

  1. A7   P 1 V 1
  2. B8   P 1 V 1
  3. C9   P 1 V 1
  4. D10   P 1 V 1

Correct answer

C. 9   P 1 V 1

Step-by-step solution

As P ∝ V ∴ P V - 1 = c o n s t a n t Also, C = C v - R x - 1 = 5 2 R - R - 1 - 1 = 3 R But as   rms speed is doubled therefore temperature becomes four times. Hence, Q = n c ∆ T = n × 3 R × 3 T 1 = 9 n R T i = 9   P 1 V 1

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