Questions

The correct answer is:

✅ "adding heat to the system"

Explanation:

The internal energy ($U$) of a system is governed by the first law of thermodynamics:

$\Delta U=q+w$

where:

• $\Delta U$ = change in internal energy

• $q$ = heat added to the system ($+q$ increases $U$, $-q$ decreases $U$)

• $w$ = work done on the system ($+w$ increases $U$, $-w$ decreases $U$)

Evaluating the answer choices:

1. "Having the system do work on the surroundings" → ❌ Incorrect

   • When the system does work on the surroundings, $w$ is negative, decreasing $U$.

2. "Adding heat to the system and having the system do work on the surroundings" → ❌ Incorrect

   • While adding heat increases $U$, the work done by the system reduces $U$, making the net effect uncertain.

3. "A volume compression" → ✅ Potentially correct, but not the best answer

   • If the volume decreases (compression), the surroundings do work on the system, increasing $U$.

   • However, this depends on whether work dominates over other effects.

4. "Withdrawing heat from the system" → ❌ Incorrect

   • Removing heat (negative $q$) decreases $U$.

5. "Adding heat to the system" → ✅ Correct

   • Heat added to the system (positive $q$) directly increases $U$, regardless of work effects.

Thus, the best choice is "adding heat to the system".