An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume \[{{V}_{1}}\] and contains ideal gas at pressure \[{{P}_{1}}\], and temperature \[{{T}_{1}}\] The other chamber has volume \[{{V}_{2}}\] and contains ideal gas at pressure \[{{P}_{2}}\] and temperature \[{{T}_{2}}\] If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be

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