Final answer:
The change in internal energy (ΔU) is not zero at constant temperature for an ideal gas when the number of moles (n) changes, due to the work associated with volume change. This is why the enthalpy change (ΔH) is ΔU plus RTΔn, even at constant temperature.
Step-by-step explanation:
The student is curious about the relationship between the change in enthalpy (ΔH) and the change in internal energy (ΔU) for an ideal gas at constant temperature.
Specifically, the query concerns why the change in internal energy (ΔU) is not considered to be zero when temperature is held constant.
This relates to the first law of thermodynamics, which states that the change in the internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings.
As a property of state functions, internal energy depends only on the current state of the system, not on the path it took to get there.
For an ideal gas, the internal energy is dependent solely on temperature; however, explaining why ΔU is not zero at constant temperature requires considering changes in the number of moles (n).
If the number of moles of gas changes while temperature remains constant, there can still be a change in internal energy because there is a change in the magnitude of the substance present. This is why we use the relation ΔH = ΔU + RTΔn to describe the change in enthalpy at constant temperature even for an ideal gas.
The term RTΔn accounts for the work done as the system's volume changes due to the change in the number of moles at constant temperature and pressure, which impacts the internal energy.
The enthalpy change for an ideal gas when only the number of moles (n) changes at constant temperature is thus not solely based on the heat flow at constant pressure but also takes into account the work done due to volume change associated with moles change. This is why ΔU is not zero and the relationship ΔH = ΔU + RTΔn holds.