When does the change in enthelpy=change in internal energy?

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SUMMARY

The relationship between enthalpy change (ΔH) and internal energy change (ΔU) is defined by the conditions of the system. In a bomb calorimeter, ΔU equals ΔH when the number of moles of gas remains constant, as there is no change in volume or pressure. However, in processes like irreversible expansion of a perfect gas, ΔH can differ from ΔU due to temperature changes, represented by the equation ΔH = ΔU + nRΔT. This indicates that ΔH = ΔU is not universally applicable and is contingent upon specific conditions such as constant temperature and pressure.

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  • Understanding of thermodynamic concepts, specifically enthalpy and internal energy.
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  • Knowledge of calorimetry, particularly bomb calorimetry and its applications.
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Sometimes in my book, a problem justifies ΔU=ΔH for a process, such as combustion in a bomb calorimeter, by saying that since the number of moles of gas doesn't change, they are equal.

In other questions, the number of moles doesn't change (such as an irreversible expansion of a perfect gas) but still, ΔH is different from ΔU because there is a change in temperature, so ΔH= ΔU + Δ(nRT)= ΔU + nRΔT

When do you use the first justification? Only in a bomb calorimeter? Any time I am given a reaction and the change in molar internal energy for that reaction where the moles of gas is the same on both sides of the equation? Does this mean that the temperature of a sample in a bomb calorimeter is constant?
 
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H = U + PV, so ΔH = ΔU whenever Δ(PV) = 0.
 

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