Question

One mole of an ideal diatomic gas undergoes a transition from A to B along a path AB as shown. The change in internal energy of the gas during the transition is

• A. \(20\ \text{kJ}\)
• B. \(-20\ \text{kJ}\)
• C. \(20\ \text{J}\)
• D. \(-12\ \text{kJ}\)

Hint:

Read the pressure and volume at A and B from the graph, then use the change in internal energy equal to five halves of the change in PV for a diatomic gas.

Answer 1

The Correct Option is B

Step 1: Use Ideal Gas Law
For one mole, $nR\Delta T=\Delta(PV)=12-20=-8\ \text{kJ}$.

Step 2: Apply Heat Capacity
$\Delta U=\frac{5}{2}nR\Delta T$ for a diatomic gas.

Step 3: Substitute
$\Delta U=\frac{5}{2}\times(-8)=-20\ \text{kJ}$.

Final Answer:
The change in internal energy is minus 20 kJ. \[ \boxed{\text{(B) }-20\ \text{kJ}} \]