To determine the change in internal energy ($\Delta U$), we apply the First Law of Thermodynamics, which is mathematically expressed as $\Delta U = q + w$ .

1. Work ($w$): According to the IUPAC sign convention used in thermodynamics, work done on the system (such as during compression or contraction) is assigned a positive sign . Therefore, $w = +462$ J.
2. Heat ($q$): Heat evolved (released) by the system to the surroundings is assigned a negative sign . Therefore, $q = -128$ J.
3. Calculation: Substituting these values into the first law equation: $\Delta U = (-128\text{ J}) + (+462\text{ J}) = +334\text{ J}$.

The internal energy of the system increases by 334 joules, which matches Option C.