$5$ moles of an ideal gas at $100\mathrm{ }\mathrm{K}$ are allowed to undergo reversible compression till its temperature becomes $200\mathrm{ }\mathrm{K}.$ If ${\mathrm{C}}_{\mathrm{V}}=28\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{K}}^{-1},$ calculate $∆\mathrm{U}$ and $∆\mathrm{p}\mathrm{V}$ for the process. $(\mathrm{R}=8.0\mathrm{ }\mathrm{J}\mathrm{ }{\mathrm{K}}^{-1}\mathrm{ }\mathrm{m}\mathrm{o}{\mathrm{l}}^{-1})$

• A

  $∆\mathrm{U}=14\mathrm{ }\mathrm{J};\mathrm{ }∆\left(\mathrm{p}\mathrm{V}\right)=0.8\mathrm{ }\mathrm{J}$
• B

  $∆\mathrm{U}=14\mathrm{ }\mathrm{kJ};\mathrm{ }∆\left(\mathrm{p}\mathrm{V}\right)=18\mathrm{ }\mathrm{kJ}$
• Correct answer
  C

  $∆\mathrm{U}=14\mathrm{ }\mathrm{kJ};\mathrm{ }∆\left(\mathrm{p}\mathrm{V}\right)=4\mathrm{ }\mathrm{kJ}$
• D

  $∆\mathrm{U}=2.8\mathrm{ }\mathrm{kJ};\mathrm{ }∆\left(\mathrm{p}\mathrm{V}\right)=0.8\mathrm{ }\mathrm{kJ}$

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