Question

Calculate the change in internal energy if an ideal gas expands from \(0.5 \text{dm}^3\) to \(3.5 \text{dm}^3\) at constant pressure 2 bar by absorbing 1800 J heat energy.

• A. \(1200\) J.
• B. \(-1200\) J.
• C. \(2400\) J.
• D. \(-2400\) J.

Hint:

Find the work from -P times the volume change, then use the first law.

Answer 1

The Correct Option is A

Step 1: Energy bookkeeping
The gas takes in 1800 J as heat. Part of this energy is spent pushing the surroundings back as the gas expands, and the rest stays inside the gas as internal energy.

Step 2: Energy spent on expansion
Pressure is 2 bar, which is $2\times10^{5}$ Pa. The volume change is $3.0\ \text{dm}^3=3.0\times10^{-3}\ \text{m}^3$.
\[ P\Delta V=2\times10^{5}\times3.0\times10^{-3}=600\ \text{J} \]

Step 3: What is left
\[ \Delta U = 1800 - 600 = 1200\ \text{J} \]
The gas stores 1200 J. The sign is positive because the heat taken in is larger than the work done, which is option (A).

Final Answer:
The change in internal energy is +1200 J, option (A). \[ \boxed{1200\ \text{J}} \]