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JEE MainPhysicsKinetic Theory of Gases

An ideal gas undergoes a reversible adiabatic expansion. During the process, it is observed that the pressure of the gas is directly proportional to the ( 7 2 )^ th power of its absolute temperature. Identify the gas from the following options:

Options

  1. AHe
  2. BCO ₂
  3. CNH ₃
  4. DN ₂

Correct answer

D. N ₂

Step-by-step solution

For an adiabatic process, the relationship between pressure P and temperature T is given by P^ 1- T^ = constant . This can be rearranged to express P in terms of T : P^ 1- T^ - P T^ -1 Given that P T^ 7/2 , we can equate the exponents: -1 = 7 2 Solving for : 2 = 7 - 7 5 = 7 = 7 5 = 1.4 A specific heat ratio of = 1.4 corresponds to a rigid diatomic gas. Among the given options, N ₂ is a diatomic gas, while He is monatomic ( = 5/3 ), and CO ₂ and NH ₃ are polyatomic. Answer: N ₂

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