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MHT CET202522 Apr 2025Evening ShiftPhysicsThermodynamicsActual

A monoatomic ideal gas, initially at temperature T₁ is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature T₂ . If L₁ and L₂ are the lengths of the gas columns before and after expansion respectively, then (T₂ / T₁ ) is given by

Options

  1. AL ₁ ~L ₂
  2. BL ₂ ~L ₁
  3. C( L ₁ ~L ₂ )^ 2 / 3
  4. D( L ₂ ~L ₁ )^ 2 / 3

Correct answer

C. ( L ₁ ~L ₂ )^ 2 / 3

Step-by-step solution

The adiabatic relation for an ideal gas is TV^ -1 = constant , where = C_p/C_v . For a monoatomic gas, = 5/3 and thus - 1 = 2/3 . Since T₁V₁^ 2/3 = T₂V₂^ 2/3 , the temperature ratio is T₂ T₁ = ( V₁ V₂ )^ 2/3 . With constant cross-sectional area, volume is proportional to length: V L . Therefore, V₁ V₂ = L₁ L₂ and T₂ T₁ = ( L₁ L₂ )^ 2/3 . This corresponds to option C .

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