1.3.1: Calorimeter- Isobaric
An isobaric calorimeter is designed to measure the heat accompanying the progress of a closed system from state (I) to state (II) at constant pressure. [1] It follows from the first law that if only ‘\(p-\mathrm{V}\)’ work is involved,
\[\Delta \mathrm{U}=\mathrm{q}-\mathrm{p} \, \Delta \mathrm{V} \nonumber \]
By definition the enthalpy \(\mathrm{H}\) of a closed system is given by equation (b);
\[\mathrm{H}=\mathrm{U}+\mathrm{p} \, \mathrm{V} \nonumber \]
\[\text { Then, } \Delta \mathrm{H}=\Delta \mathrm{U}+\mathrm{p} \, \Delta \mathrm{V}+\Delta \mathrm{p} \, \mathrm{V} \nonumber \]
Hence from equations (a) and (c), at constant pressure,
\[\Delta \mathrm{H}=\mathrm{q} \nonumber \]
\[\text { Thus at constant pressure, } \Delta \mathrm{H}=\mathrm{H}(\mathrm{II})-\mathrm{H}(\mathrm{I})=\mathrm{q} \nonumber \]
Hence if we record the heat (exothermic or endothermic) at constant pressure we have the change in enthalpy, \(\Delta \mathrm{H}\). [2] Equation (e) highlights the optimum thermodynamic equation. On one side of the equation is a measured property/change and on the other side of the equation is a change in a property of the system which we judge to be informative about the chemical properties of a system; e.g. \(\Delta \mathrm{H}\). The problem is that the derived property is not the actual change in energy, \(\Delta \mathrm{U}\).
Footnotes
[1] W. Zielenkiewicz, J.Therm. Anal.,1988, 33 , 7.
[2] Hess’ Law. This law is a consequence of the observation that the enthalpy of a closed system is a state variable. \(\Delta \mathrm{H}\) accompanying the change from state I to state II is independent of the number of intermediary states and of the general path between the two states and the rate of change.
[3] Isothermal calorimetry
- I. Wadso, Chem. Soc. Rev.,1997,26,79.
- I. Wadso, in Experimental Thermodynamics, IUPAC Data Series No. 39; volume 4, ed. K. N. Marsh and P. A. G. O’Hare, chapter 12, Blackwell, Oxford,1994.
- I. Wadso, in Thermal and Energetic Studies of Cellular Systems, ed. A. M. James, Wright, Bristol, 1987, chapter 3.
- J. B. Ott and C. J. Wormwald, in Experimental Thermodynamics, 2 IUPAC Data Series No. 39; ed. K. N. Marsh and P. A. G. O’Hare, chapter 8, Blackwell, Oxford,1994.
- S. J. Gill, J. Chem.Thermodynamics, 1988, 20 ,1361.