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JEE Main 20179 AprilOnline
Exam
JEE Main
Year
2017
Date
9 April
Mode
Online
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2017 · 9 April · Online · Physics · Kinetic Theory of Gases

N moles of diatomic gas in a cylinder is at a temperature T . Heat...

NN moles of diatomic gas in a cylinder is at a temperature TT. Heat is supplied to the cylinder such that the temperature remains constant but nn moles of the diatomic gas get converted into monoatomic gas. The change in the total kinetic energy of the gas is

Options

  1. A00
  2. B52nRT\dfrac{5}{2}nRT
  3. C32nRT\dfrac{3}{2}nRT
  4. D12nRT\dfrac{1}{2}nRT

Correct answer

D. 12nRT\dfrac{1}{2}nRT

Step-by-step solution

Initial kinetic energy of the system,

Ui=N52RT{U}_{i} = N\dfrac{5}{2}RT

Final kinetic energy of the system,

Uf=2n32RT+(N−n)52RT{U}_{f} = 2n\dfrac{3}{2}RT + \dfrac{\left(N - n\right)5}{2}RT

⇒Uf=12nRT+52NRT⇒ {U}_{f} = \dfrac{1}{2}nRT + \dfrac{5}{2}NRT

\DeltaU=Q=12nRT\DeltaU = Q = \dfrac{1}{2}nRT.
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