One mole of an ideal gas passes through a process where pressure and volume obey the relation $\mathrm{P}={\mathrm{P}}_{\mathrm{o}}\left[1-\frac{1}{2}{\left(\frac{{\mathrm{V}}_{\mathrm{o}}}{\mathrm{V}}\right)}^2\right]$ . Here ${\mathrm{P}}_{\mathrm{o}}$ and ${\mathrm{V}}_{\mathrm{o}}$ are constants. Calculate the change in the temperature of the gas if its volume changes from ${\mathrm{V}}_{\mathrm{o}}\mathrm{ }$ to $2{\mathrm{V}}_{\mathrm{o}}$ .