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 $2{\mathrm{V}}_{\mathrm{o}}$ .

• A

  $\frac{1}{4}\frac{{\mathrm{P}}_0{\mathrm{V}}_0}{\mathrm{R}}$
• Correct answer
  B

  $\frac{5}{4}\frac{{\mathrm{P}}_0{\mathrm{V}}_0}{\mathrm{R}}$
• C

  $\frac{1}{2}\frac{{\mathrm{P}}_0{\mathrm{V}}_0}{\mathrm{R}}$
• D

  $\frac{3}{4}\frac{{\mathrm{P}}_0{\mathrm{V}}_0}{\mathrm{R}}$

Hence, the correct answer is option: 'B'.