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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 11 and 22 are filled with air at temperatures (T1,T2),(T_1, T_2), volume (V1,V2)(V_1, V_2) and pressure (P1,P2)(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)

  1. Vessels are insulated, so internal energy is conserved: (n1+n2)CvT=n1CvT1+n2CvT2(n_1 + n_2)C_vT = n_1C_vT_1 + n_2C_vT_2.
  2. With n=PVRTn = \frac{PV}{RT}: T=P1V1+P2V2P1V1/T1+P2V2/T2T = \frac{P_1V_1 + P_2V_2}{P_1V_1/T_1 + P_2V_2/T_2}.
  3. T=T1T2(P1V1+P2V2)P1V1T2+P2V2T1T = \frac{T_1T_2(P_1V_1 + P_2V_2)}{P_1V_1T_2 + P_2V_2T_1}
  4. So the answer is (a).
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