The volume of the reaction vessel within a bomb calorimeter is fixed. This means that the heat flow between the reaction vessel and the surrounding water bath must equal the internal energy change within it. In other words, none of the change in internal energy goes into pressure-volume work.
One important thing to consider when applying the 1st law to chemistry is that internal energy is a much richer idea in chemistry. In physics, we kept pretty much to the ideal gas whose internal energy is only the kinetic energy of the particles. In chemistry, though, the internal energy is much more complicated. It helps to understand that there really are two primary kinds of internal energy relevant to chemistry. These are the kinetic energy, which will have rotational and vibrational modes in addition to translational modes in most chemical substances, and the electrostatic potential energy associated with the arrangement of charged particles (the protons and electrons in a particular atomic, molecular, or intermolecular arrangement). Crucial to being able to conceptualize chemical change in the context of the First Law of Thermodynamics is a clear sense of the electrostatic potential energy changes in chemical substances as they impact internal energy change. Which bonds are broken? Which bonds are formed? To understand the internal energy changes associated with a chemical process you have to look at the rearrangement of charge in the new bonding or intermolecular state of the system.
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