Depending on how sensitive the measure is, and how detailed the answer should be:
- The simpler and directly usable answer is "copper doesn't oxidize"
- But if considering the energy brought by heat, some copper can oxidize and quickly reduce to metal.
Trying to model how long a Cu2+ or Cu+ would survive, by estimation of shocks and so on, would be unmanageable. Fortunately, we have thermodynamics. It doesn't tell the absolute value from zero assumption but does permit many predictions from a small set of measures.
From the thermo data (H, S, G) of copper ions in water, which compare to metallic copper, you can predict numerically the concentration of dissolved copper ions at equilibrium.
A simpler approach would compare the 340mV with the temperature (300K is equivalent to 26meV) to tell that the concentration is tiny, being squeezed by a factor resembling exp(-340/26).