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: Understanding the Concept
The first law of thermodynamics is \(\Delta U=q+w\), where \(w\) is work done on the system. For expansion against constant pressure, work is done by the gas, so \(w\) is negative.

Step 2: Key Formula or Approach
\[ w=-P_{ext}\Delta V,\qquad \Delta U=q+w \]

Step 3: Work done
\[ \Delta V=3.5-0.5=3.0\ \text{dm}^3 \]
\[ w=-2\ \text{bar}\times3.0\ \text{dm}^3=-6\ \text{bar dm}^3 \]
Since 1 bar dm\(^3\) = 100 J, this gives \(w=-600\) J.

Step 4: Apply the first law
The system absorbs heat, so \(q=+1800\) J.
\[ \Delta U=1800+(-600)=1200\ \text{J} \]

Step 5: Why the others are wrong
Option (B) has the wrong sign. Options (C) and (D) come from adding the 600 J incorrectly or from doubling the answer. Only \(+1200\) J follows from the first law.

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