Two thermally insulated vessels 1 and 2 are filled with air at temperatures \[\] volume \[({{V}_{1}},\text{ }{{\text{V}}_{2}})\]and pressure \[({{P}_{1}},\text{ }{{\text{P}}_{2}})\] respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

• A. \[{{T}_{1}}+{{T}_{2}}\]
• B. \[({{T}_{1}}+{{T}_{2}})/2\]
• C. \[\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{2}}+{{P}_{2}}{{V}_{2}}{{T}_{1}}}\]
• D. \[\frac{{{T}_{1}}{{T}_{2}}\left( {{P}_{1}}{{V}_{1}}+{{P}_{2}}{{V}_{2}} \right)}{{{P}_{1}}{{V}_{1}}{{T}_{1}}+{{P}_{2}}{{V}_{2}}{{T}_{2}}}\]