Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T_0 , while Box B contains - Physics MCQ AIEEE 2006 2026 | ExamTest.live

hardMCQAIEEE 20062026Physics

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Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T_{0}, while Box B contains one mole of helium at temperature (7/3) T_{0} . The boxes are put into thermal contact. The final temperature T_{f} is:

Solution & Step-by-step Explanation

Internal energy is conserved: Δ U_{A} + Δ U_{B} = 0 . n_{1} C_{v 1} (T_{f} - T_{01}) + n_{2} C_{v 2} (T_{f} - T_{02}) = 0 .Nitrogen (N_{2}): n_{1} = 1, C_{v 1} = \frac{5}{2} R, T_{01} = T_{0} .Helium (He): n_{2} = 1, C_{v 2} = \frac{3}{2} R, T_{02} = \frac{7}{3} T_{0} . 1 \cdot \frac{5}{2} R (T_{f} - T_{0}) + 1 \cdot \frac{3}{2} R (T_{f} - \frac{7}{3} T_{0}) = 0 \frac{5}{2} T_{f} - \frac{5}{2} T_{0} + \frac{3}{2} T_{f} - \frac{7}{2} T_{0} = 0 4 T_{f} - 6 T_{0} = 0 ⟹ 4 T_{f} = 6 T_{0} ⟹ T_{f} = \frac{3}{2} T_{0} .

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Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature T_{0}, while Box B contains one mole of helium at temperature (7/3) T_{0} . The boxes are put into thermal contact. The final temperature T_{f} is:

2 T_{0}

(7/3) T_{0}

(3/2) T_{0}

(2/3) T_{0}

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