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^{3}and the pressure stays at 5kPa.

If the work done by the gas is the pressure times the change in volume we get 5000J, but if we apply the ideal gas law to that equation, we get nRΔT, which then gives an amount of 415.5J. In the first instance, the change in internal energy decreases which is weird to me. In the second, it acts accordingly and increases.

What is the fundamental issue I am having dealing with this concept, and why do we effectively learn two ways of calculating gas processes?

Thanks in advance. For some reason, Thermodynamics is kicking my butt because I can't conceptualize it correctly.