How is temperature inside a bomb calorimeter constant?

Question

I've looked around and have been unable to find an answer.

When determining molar reaction enthalpy, you first perform the reaction in the steel bomb then measure the temperature change of the water to calculate the molar energy released from the reaction. Then you add $\mathrm{\Delta(PV)}$ to $\mathrm{\Delta U}$ to calculate molar reaction enthalpy. $\mathrm{\Delta(PV)}$ is then said to equal $\mathrm{\Delta n\,RT}$, where temperature is constant.

But, if for example the reaction raises the temperature in the steel bomb from 25 °C to 40 °C and eventually the temperature equilibrates so that the temperature of the water is 28 °C and the temperature inside the steel bomb is 28 °C, doesn't the $\mathrm{\Delta U}$ value underestimate the energy change of the reactants since the temperature inside the bomb is raised as well and shouldn't $\mathrm{\Delta(PV) = \Delta(n)R\Delta(T)}$?

Answer 1

Yes, any increase in the reaction product mixture temperature results in a small inaccuracy in the calculated heat of reaction. But, it is really pretty small, and you can correct it by calculating the amount of heat that needs to be removed for the products to be at the same temperature as the reactant mixture.