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JEE Main 2006
Exam
JEE Main
Year
2006
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2006 · Physics · Kinetic Theory of Gases

Two rigid boxes containing different ideal gases are placed on a...

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T0T_0, while Box BB contains one mole of helium at temperature (7/3)T0(7 / 3) T_0. The boxes are then put into thermal contact with each other and heat flows between them until the gases reach a common final temperature. (Ignore the heat capacity of boxes). Then, the final temperature of the gases, TfT_f, in terms of T0T_0 is

Options

  1. ATf=52 T0\mathrm{T}_{\mathrm{f}}=\frac{5}{2} \mathrm{~T}_0
  2. BTf=37 T0\mathrm{T}_{\mathrm{f}}=\frac{3}{7} \mathrm{~T}_0
  3. CTf=73 T0\mathrm{T}_{\mathrm{f}}=\frac{7}{3} \mathrm{~T}_0
  4. DTf=32T0T_f=\frac{3}{2} T_0

Correct answer

D. Tf=32T0T_f=\frac{3}{2} T_0

Step-by-step solution

ΔU=0\Delta \mathrm{U}=0 ⇒32R\Rightarrow \frac{3}{2} \mathrm{R}\left(\mathrm{T}_{\mathrm{f}}-\mathrm{T}_0\right)+1 \times \frac{5}{2} \mathrm{R}\left(\mathrm{T}_{\mathrm{f}}-\frac{7}{3} \mathrm{~T}_0\right)=0 \mathrm{~T}_{\mathrm{f}}=\frac{3}{2} \mathrm{~T}_0
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