A gas sample can reach the same pressure, volume and temperature by many different histories of heating, cooling, compressing or expanding. What does the source say about how the internal energy U depends on that history?
AU changes only if heat transfer occurred somewhere along the way
BU depends on the total distance the piston traveled
CU is larger for histories that take place more slowly
DU depends only on the state of the system, not on how it got there
Answer & Solution
Correct answer: D. U depends only on the state of the system, not on how it got there
1. Internal energy is a state function, so its value is fixed by the system's current pressure, volume and temperature alone.
2. This is stated directly: the internal energy U of a system depends only on the state of the system and not how it reached that state.
3. Whether heat transfer occurred, and how much, changes Q but does not by itself determine U, so option A confuses the state function with one of the path-dependent quantities that can produce it.
4. The distance a piston travels and the speed of a process affect how work and heat get distributed along the way, but they do not change the state U depends on, ruling out options B and C.
_Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.1 The First Law of Thermodynamics_
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