Question

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

• A. The change in internal energy in whole cyclic process is \(250R\)
• B. The change in internal energy in the process CA is \(700R\)
• C. The change in internal energy in the process AB is \(-350R\)
• D. The change in internal energy in the process BC is \(-500R\)

Hint:

Internal energy change depends only on temperatures: use \(\Delta U=nC_{v}\Delta T\) with \(C_{v}=\frac{5R}{2}\) for each process.

Answer 1

The Correct Option is D

Step 1: Formula
$\Delta U=nC_{v}\Delta T$ with $n=1$ and $C_{v}=\frac{5R}{2}$.

Step 2: Process BC
$T_{B}=800$ K and $T_{C}=600$ K, so $\Delta U_{BC}=\frac{5R}{2}(-200)=-500R$.

Step 3: Check the others
The whole cycle has $\Delta U=0$, $\Delta U_{AB}=+1000R$ and $\Delta U_{CA}=-500R$, so the other options do not hold. Option (D) is correct.

Final Answer:
Only the statement about process BC is correct. \[ \boxed{\text{(D) }\text{The change in internal energy in the process BC is }-500R} \]