Multiple choice

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

  1. $T_1\,+\, T_2$
  2. $(T_1\, +\, T_2)/2$
  3. $\displaystyle \frac{T_1\, T_2\, P(V_1\, +\, V_2)}{P_1V_1T_2\, +\, P_2V_2T_1}$
  4. $\displaystyle \frac{T_1\, T_2\, (P_1V_1\, +\, P_2V_2)}{P_1V_1T_2\, +\, P_2V_2T_1}$
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C Correct answer
AI explanation

For the mixing of ideal gases in an insulated rigid vessel, the total number of moles remains constant and the internal energy is conserved. By conserving the total moles, the common pressure P is used to find the equilibrium temperature formula. The final equilibrium temperature calculates to (T1 T2 P(V1 + V2)) divided by (P1V1T2 + P2V2T1).

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