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JEE Main 2004 (AIEEE) · Gas Laws & Ideal Gas Equation

Gas Laws & Ideal Gas Equation question from JEE Main 2004 (AIEEE)

Q82JEE Main 2004 · AIEEEDifficult

Gas Laws & Ideal Gas Equation

Two thermally insulated vessels $1$ and $2$ are filled with air at temperatures $(T_1, T_2),$ volume $(V_1, V_2)$ and pressure $(P_1, P_2)$ respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

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Answer: (a)

Vessels are insulated, so internal energy is conserved: $(n_1 + n_2)C_vT = n_1C_vT_1 + n_2C_vT_2$ .
With $n = \frac{PV}{RT}$ : $T = \frac{P_1V_1 + P_2V_2}{P_1V_1/T_1 + P_2V_2/T_2}$ .
$T = \frac{T_1T_2(P_1V_1 + P_2V_2)}{P_1V_1T_2 + P_2V_2T_1}$
So the answer is (a).

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