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Yes, when a system is isothermal it means that there is no temperature change in the system and thus the temperature would be constant. Only for ideal gases does this mean that the change in internal energy is 0 because, for ideal gases, and (Anything multiplied by 0 equals 0).
A good way to remember the types of systems is to break apart the word, so iso: same and thermal: temperature-related. Since the temperature is the same throughout the reaction, it would follow that Tf - Ti would equal 0. Then, in calculation, your change in internal energy would also be 0.
But when an ideal gas expands isothermally, volume increases and pressure decreases. Since volume increased, the system did work on the surroundings...so wouldn't work be non-zero, making the change in internal energy non-zero as well?
Internal energy is a state function, but work is not. Therefore, how the change in internal energy occurred doesn't matter since it will always be 0 in isothermal system. However, the path that work takes is important and needs to be calculated, since it doesn't always equal 0 in an isothermal system. the only thing we know for sure is that q=-w in isothermal system.
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