Application Question
Medium difficulty • Concept in a practical situation
Question 1
Applied ConceptA student performs an experiment where 1 kJ of work is done on an adiabatic system by rotating paddle wheels (mechanical work). In a second experiment, the same system is returned to its initial state and 1 kJ of electrical work is done using an immersion rod. Compare the final states in both experiments.
- In both experiments, the same amount of work (1 kJ) is done on the same adiabatic system (q = 0), so ΔU = wad = +1 kJ in each case — the change in internal energy is identical.
- This demonstrates Joule's finding that ΔU depends only on the initial and final states, not on how the work is done (path-independence), confirming that internal energy is a state function.
- Since ΔU is the same (both states reached have the same internal energy), the temperature rise ΔT will be identical in both experiments, as measured by a thermometer immersed in the system.
- This path-independence is the foundational experimental basis for defining U as a state function and for the first law of thermodynamics.
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