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Internal energy is due to motion of particles in a system which depends on temperature. As you mentioned, temperature in isothermal process is constant, so the internal energy will also be constant. Therefore, the change in internal energy 0. Hope that helps!
furthermore, it is important to note that for isothermal, reversible processes, the change in internal energy is 0 when they are ideal gases. Because they are ideal gases, there is no exhange in energy during the collisions.
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