Two thermally insulated vessels 1 and 2 are filled with air at temperatures (T1, T2), volume (V1, V2) and pressure (P1, P2) respectively. If the valve joining two vessels is opened, the temperature inside the vessel at equilibrium will be
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T1 + T2
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T1 + T2/2
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C.

There will be no change in number of moles if the vessels are joined by the valve. Therefore, from gas equation
Now, according to Boyle's law (pressure = constant) P1 V1 + P2 V2 = P(V1 + V2 )