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Yes. In addition, bomb calorimeter is an isolated system, so neither the matter nor the energy could be exchanged between the system (inside of bomb calorimeter) and the surrounding (outside of the bomb calorimeter). Therefore, the internal energy of bomb calorimeter is constant.
A bomb calorimeter is a closed system, which means that there is no net change in volume. Since there is no change in volume there isn't any work being done and the change in internal energy (delta U) should be equal to q
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