Question 166 of 190

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 :

AThe change in internal energy in whole cyclic process is 250 RBThe change in internal energy in the process CA is 700 R.CThe change in internal energy in the process AB is - 350 RDThe change in internal energy in the process BC is - 500 R

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Answer: (D) The change in internal energy in the process BC is - 500 R

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

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

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