When conceptually interpreting the internal energy change involved in a chemical process, the first step is to judge the electrostatic potential energy changes that occur with the realignment of the charged particles between the initial and final states. What are the changes in the relative position of charge densities (electrons and protons) at the atomic level. What has changed at the the molecular level or intermolecular molecular level? This can often lead directly to predicting the internal energy changes that occur through a chemical reaction or other type of chemical transformation such as a phase change or solution process.
Note that along with the collective electrical potential energy of the charged particles, the kinetic energy, which they possess through their motion, is the other major form of chemical internal energy. Kinetic energy is distributed in partitions or modes of translational, rotational and vibrational motion.
Although you must always keep in mind that the interactions are governed by quantum mechanics, for most purposes a basic view of electrostatic potential energy change is often sufficient to predict whether or not a system has gained or lost energy through a particular transformation.
Often the next step in chemical analysis is to move from the particle level approach to electrostatic potential energy and particle kinetic energy to the macrostate perspective of thermochemistry and ask how the internal energy changes we have analyzed will translate into heat flow and work between the system and its surroundings. From thermochemistry, then you move on to chemical thermodynamics, in which the heat flow, or enthalpy change, is a primary conceptual operator, along with the entropy change of the system, in determining which direction the reaction will proceed on its way toward the equilibrium state. The combination of enthalpy change and entropy change in determining the direction of spontaneity is embodied in the thermodynamic quantity - the free energy of the system.
This line of reasoning, as an imaginative conceptual skill rather than a specific type of quantitative problem solving, to move in the conceptual imagination from the consideration of electrostatic potential energy changes at the particle level to internal energy change of the system to heat flow and work between the system and its surroundings, then bringing entropy into the discussion and, deriving, finally, an understanding of the free energy change really is absolutely fundamental to an understanding of chemical change. It is one of the primary conceptual arcs in physical science.
In a bomb calorimeter reactions are carried out isovolumetrically, so there is no work. In that case, the internal energy change will equal the heat flow.