Final answer:
In a bomb calorimeter, while the reaction occurs at constant volume and heat absorbed by the water equals the change in internal energy, the maintenance of constant temperature during the reaction ensures the internal energy change primarily occurs due to the transfer of heat. Although internal energy for an ideal gas depends only on temperature, the constant temperature within the calorimeter is maintained by the transfer of heat, resulting in an internal energy change associated with the heat absorbed or released by the system.
Step-by-step explanation:
In a bomb calorimeter, the constant temperature is maintained by the transfer of heat between the system (reaction occurring inside the calorimeter) and the surroundings (water in the calorimeter). While the internal energy of an ideal gas depends solely on temperature, the constant temperature condition in the calorimeter doesn't imply that internal energy remains constant. Instead, any change in internal energy is attributed to the exchange of heat between the system and the surroundings.
During a chemical reaction within the calorimeter, if the system absorbs heat, its internal energy increases. Conversely, if the system releases heat, its internal energy decreases. The constant temperature maintained in the calorimeter ensures the heat transfer causes the internal energy change while accommodating the ideal gas's dependency on temperature for its internal energy. Therefore, the heat absorbed or released during the reaction causes the change in internal energy, allowing the system to comply with the constant temperature condition.
This interplay between constant temperature and the internal energy change in an ideal gas within a bomb calorimeter highlights how the heat transfer during a reaction becomes the primary factor affecting the internal energy, enabling the system to maintain equilibrium at a constant temperature while exhibiting a change in its internal energy state.