A box contains N molecules of a perfect gas at temperature \[{{T}_{1}}\] and pressure \[{{P}_{1}}\]. The number of molecules in the box is doubled keeping the total kinetic energy of the gas same as before. If the new pressure is \[{{P}_{2}}\] and temperature \[{{T}_{2}},\] then

• A. \[{{P}_{2}}=P,\,\,{{T}_{2}}={{T}_{1}}\]
• B. \[{{P}_{2}}={{P}_{1}},\,{{T}_{2}}=\frac{{{T}_{1}}}{2}\]
• C. \[{{P}_{2}}=2{{P}_{1}},\,{{T}_{2}}={{T}_{1}}\]
• D. \[{{P}_{2}}=2{{P}_{1}},\,{{T}_{2}}=\frac{{{T}_{1}}}{2}\]