Kinetic Theory

JEE Main level, single correct, medium

166 of 168

Question 166 of 168

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

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Answer: (D) Tf=32T0T_f=\frac{3}{2} T_0

ΔU=0\Delta \mathrm{U}=0
⇒32R(Tf−T0)+1×52R(Tf−73 T0)=0\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
 Tf=32 T0\mathrm{~T}_{\mathrm{f}}=\frac{3}{2} \mathrm{~T}_0

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