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A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 ~cm ^3 and temperature 27^ C . The change in temperature when the gas is adiabatically compressed to 200 ~cm ^3 is : (Take =1.5: is the ratio of specific heats at constant pressure and at constant volume)

Options

  1. A327 K
  2. B600 K
  3. C522 K
  4. D300 K

Correct answer

D. 300 K

Step-by-step solution

aligned & V ₁=800 ~cm ^3 ~V ₂=200 ~cm ^3 & ~T ₁=300 ~K aligned for adiabatic aligned & TV ^ -1 = const. & (300)(800)^ 1.5-1 = T ₂(200)^ 1.5-1 & ~T ₂=300 [ 800 200 ]^ 0.5 =300 (2^2 )^ 1 / 2 & ~T ₂=600 ~K & ~T =600-300=300 ~K aligned

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