Differentiate between calorimetry at constant pressure and constant volume and give an example of each.

• A. Constant pressure measures ΔH (q_p ≈ ΔHrxn); constant volume measures ΔU (q_v ≈ ΔUrxn); examples: a coffee cup calorimeter (constant P) and a bomb calorimeter (constant V).
• B. Constant volume measures ΔH; constant pressure measures ΔU; examples: a coffee cup calorimeter and a bomb calorimeter.
• C. Both measure ΔH; examples: bomb and coffee cup calorimeters.
• D. Constant pressure and constant volume both measure q = m c ΔT; examples: adiabatic calorimeter for P and isochoric calorimeter for V.

Answer: (A)

When heat flows in a chemical process, the energy balance includes not only the internal energy change but also the work the system can do on its surroundings. At constant pressure, the system can expand or contract, so the heat exchanged with the surroundings equals the enthalpy change of the reaction. This makes q at constant pressure effectively equal to ΔH_rxn, because ΔH = ΔU + Δ(PV) and with constant pressure Δ(PV) ≈ PΔV, which is accounted for in the heat measured. In contrast, at constant volume no PV work is done (there is no volume change), so the heat added directly equals the internal energy change: q at constant volume equals ΔU_rxn. The practical embodiments are the coffee cup calorimeter, which is open to the surroundings and operates at essentially constant pressure, and the bomb calorimeter, which is a rigid, sealed vessel and operates at constant volume. So the best pairing is that constant pressure measures ΔH and constant volume measures ΔU, with the coffee cup giving ΔH and the bomb calorimeter giving ΔU.