One mole of diatomic ideal gas undergoes a cyclic process ABC as shown in figure. The process BC is adiabatic. The temperatures at A, B and C are 400 K, 800 K and 600 K respectively. Choose the correct statement :

• A

  The change in internal energy in whole cyclic process is 250 R
• B

  The change in internal energy in the process CA is 700 R.
• C

  The change in internal energy in the process AB is  - 350 R
• Correct answer
  D

  The change in internal energy in the process BC is  - 500 R

Solution

$\Delta {\text{U}}_{\text{CA}}={\text{nc}}_{\text{v}}\left({\text{T}}_{\text{A}}-{\text{T}}_{\text{C}}\right)=1\times \frac{5}{2}\text{R}\left(-200\right)=-500\text{R}$

$\Delta {\text{U}}_{\text{AB}}={\text{nc}}_{\text{v}}\left({\text{T}}_{\text{B}}-{\text{T}}_{\text{A}}\right)=1\times \frac{5}{2}\text{R}\times 400=+1000\text{R}$

$\Delta {\text{U}}_{\text{BC}}={\text{nc}}_{\text{v}}\left({\text{T}}_{\text{C}}-{\text{T}}_{\text{B}}\right)=1\times \frac{5}{2}\text{R}\left(-200\right)=-500\text{R}$

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