MHT CET202123 Sep 2021Morning ShiftChemistryThermodynamics (C)Actual
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 T ₂ ~T ₁ is
Options
- A[ L ₁ ~L ₂ ]^ 2 / 3
- B[ L ₁ ~L ₂ ]^ 1 / 2
- C[ L ₂ ~L ₁ ]^ 1 / 2
- 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 aligned & 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 aligned Since volume is proportional to length due to area being constant.