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MHT CET20227 Aug 2022Morning ShiftPhysicsThermodynamicsActual

A monoatomic ideal gas, initially at temperature ' T ₁ ' is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature ' T ₂ ' by releasing the piston suddenly L₁ and L₂ are the lengths of the gas columns before and after the expansion respectively. The T₂ T₁ is

Options

  1. A[ L ₁ ~L ₂ ]^ 2 / 3
  2. B[ L ₁ ~L ₂ ]^ 1 / 2
  3. C[ L ₂ ~L ₁ ]^ 1 / 2
  4. D[ L ₂ ~L ₁ ]^ 2 / 3

Correct answer

A. [ L ₁ ~L ₂ ]^ 2 / 3

Step-by-step solution

In an adiabatic process T ₁ ~V ₁^ -1 = T ₂ ~V ₂^ -1 For an ideal mono atomic gas the no of degree of freedom is 3 Y=1+ 2 f =1+ 2 3 T ₁ ~T ₂ = ( V ₂ ~V ₁ )^ Y -1 = ( V ₂ ~V ₁ )^ 2 / 3 = ( L ₂ ~L ₁ )^ 2 / 3 Since volume is proportional to length due to area being constant.

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