1.3.1: Calorimeter- Isobaric

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Michael J Blandamer & Joao Carlos R Reis
University of Leicester & Faculdade de Ciencias

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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,

\[\Delta \mathrm{U}=\mathrm{q}-\mathrm{p} \, \Delta \mathrm{V}\]

By definition the enthalpy \(\mathrm{H}\) of a closed system is given by equation (b);

\[\mathrm{H}=\mathrm{U}+\mathrm{p} \, \mathrm{V}\]

\[\text { Then, } \Delta \mathrm{H}=\Delta \mathrm{U}+\mathrm{p} \, \Delta \mathrm{V}+\Delta \mathrm{p} \, \mathrm{V}\]

Hence from equations (a) and (c), at constant pressure,

\[\Delta \mathrm{H}=\mathrm{q}\]

\[\text { Thus at constant pressure, } \Delta \mathrm{H}=\mathrm{H}(\mathrm{II})-\mathrm{H}(\mathrm{I})=\mathrm{q}\]

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.