Step 1: Understand first electron gain enthalpy.
First electron gain enthalpy is the energy change when an electron is added to a neutral atom:
\[
O + e^- \rightarrow O^-
\]
This process releases energy, hence it is negative (\(-141\,\text{kJ mol}^{-1}\)).
Step 2: Consider second electron addition.
Second electron gain enthalpy involves adding an electron to an already negatively charged ion:
\[
O^- + e^- \rightarrow O^{2-}
\]
Step 3: Analyze electrostatic repulsion.
The incoming electron experiences strong repulsion from the negatively charged ion.
This requires energy to overcome repulsion.
Step 4: Nature of second electron gain enthalpy.
Since energy is required, the process is endothermic.
Hence, second electron gain enthalpy is positive.
Step 5: Compare with first electron gain enthalpy.
First electron gain enthalpy is negative (exothermic), while second is positive (endothermic).
Step 6: Interpretation.
Addition of electron to an anion is always energetically unfavorable due to repulsion.
Step 7: Final conclusion.
\[
\boxed{\text{A positive value}}
\]