<p>The present study revisits the first, second, and combined laws of thermodynamics by introducing partial internal energy in the first law, entropy production and partial entropy in entropy change, and partial volume in the context of work exchange. These developments yield a more rigorous and internally consistent thermodynamic framework, within which chemical potential is defined as the partial derivative of internal energy with respect to composition at constant entropy and volume, and is related to partial internal energy, partial entropy, and partial volume.</p>