In a Bomb Calorimeter, we measure the change in temperature of water $\Delta T$. But when it comes to calculating the change in internal energy we use $$\Delta U = C_{cal}\Delta T$$ Where $C_{cal}$ is the specific heat capacity of the whole calorimeter. Why is that? What I mean is that we're measuring the change in temperature of the water and assuming that heat from the reaction transferred completely to water, so shouldn't we apply $$\Delta U = C_{water}\Delta T$$ since we're calculating the change in temperature of the water?
Or are we assuming that the change in temperature of the water is the change in temperature of every element in the calorimeter?