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New heat-capacity measurements are reported for four rock types; Westerly granite from Bradford, RI, andesite from Lake County, OR, peridotite from Sonoma County, CA, and basalt from the Columbia River Group. Measurements were made on powders of the rocks in the temperature range of 340 to about 1000 K. Our measured heat-capacity values for rocks and other measurements of heat capacity or heat content of rocks found in the literature have been compared with estimated rock heat capacities calculated from the summation of heat capacities of both minerals and oxide components. The validity of calculating the heat content or heat capacity of rocks to better than about ± 3% from its mineral or chemical composition is well demonstrated by the data presented here. Introduction Knowledge of the heat content (J^mol"1 ) and/or heat capacity (J-mol'^K" 1 , or specific heat, J^g'^K"1 ) of rocks and minerals is necessary for modelling, controlling, redesigning and refining, and developing industrial processes and in modelling and interpreting geologic processes. Such processes range from extraction of elements such as aluminum and vanadium from rock; to modelling the evolution of subducting plates and generation of magma; to containment of radioactive and hazardous waste. Examples drawn from recent literature include Somerton (1992) who describes the use of heat capacity data as applied to the recovery of petroleum from old or low yield reservoirs and Jacobs et al. (1992) who describe "In Situ Vitrification" as a method of containing radioactive and hazardous waste. The heat content is the quantity of most general use in the types of calculations cited above. Although commercial instrumentation for the direct measurement of heat capacities at super ambient temperatures has been available for about 20 years, most of the super ambient data for minerals and rocks have been developed using drop calorimeters that measure the heat content. The heat capacity is the first derivative of the heat content. Good heat capacity measurements can easily be integrated to give better detail in the heat content than can be obtained from direct heat-content measurements, and this may be critical for some processes. Measured heat-content values are commonly known to ±0.5%, but the first derivative has a larger uncertainty and the derived values can vary with the form of the fitting equation. Where heat-capacity values are critical to a process, derivation of the heat capacity must be done carefully. Few measurements of the heat capacity or heat content of rocks are available. Measurement of one of these properties for all the compositions of rocks for which model calculations may be necessary is a much more time consuming and expensive task than calculation of the quantity to the accuracy necessary from data that already exist. This report provides a method for estimating the heat capacity of rocks to better than ± 5%. Measured rock heat capacity or heat content Previous measurements of the heat capacity or heat content of rocks are essentially limited to the following studies. Lindroth and Krawza (1971) published heat-content values for six rock types at temperatures between 25° and 1000°C (St. Cloud gray granodiorite, Holston limestone, Sioux quartzite, Rockville quartz monzonite, Salem limestone, and Dresser basalt). Somerton (1958) graphically presented heat-capacity values at temperatures between 77° and 1000°F for six rock types that were calculated from heat-content measurements (sandstone, two silty sands, two siltstones, and shale). Somerton (1992) presented the experimental values from Somerton (1958) in tabular form. Robie et al. (1970), Robie and Hemingway (1971), and Hemingway et al. (1973) published heat-capacity values for lunar basalts and soils for temperatures between 90 and 350 K. Goranson (1942) lists heat capacity values for rocks derived from pre-1925 literature and some estimates. The data are for the temperature range of 0° to 1200° C, but chemical or mineralogical characterization of the samples is poor. Estimating the heat capacity and heat content of rocks Modifications of the Neumann-Kopp rule (Swalin, 1962) to estimate heat capacities have been cited in several studies (Somerton, 1958 and 1992; Wechsler and Glaser, 1964; and Lindroth and Krawza, 1971). The rule states that the heat capacity of a solid can be calculated from the weighted sum of the heat capacities of the elements forming the solid. Wechsler and Glaser (1964) claim that specific heats for nearly all rock systems may be calculated to ±10% using this rule. However, for the refinement of industrial processes and for other studies ±10% is not adequate. Somerton (1958, 1992) modified the rule and used the heat capacities of oxides to calculate specific heats for the sedimentary rock types listed above. Somerton found agreement to ±2% between measured and calculated specific heats. He calculated fictive values for oxide components such as H2O and CO2 that have standard states (liquid and gas) that differ from the state of those components in the rock by taking the difference in the heat capacities between an hydroxide or carbonate phase and the corresponding oxide phase, that is Mg(OH) 2 MgO or CaC03 CaO. Finally, Lindroth and Krawza (1971) argued that heat capacities or heat contents must be measured to be accurate, citing variations in rock structure and composition that can effect the representative chemical and mineralogical analyses as critical factors. This study corroborates the use of the modified Neumann-Kopp rule for estimating heat contents, heat capacities or specific heats for rocks from their chemical analyses. We have measured the specific heats of four U.S. Geological Survey standard rock samples (Chayes, 1951; Schlecht and Stevens, 1951; and Flanagan, 1967) and have compared the calculated values with those measured values. Similar comparisons were made between the measured values obtained from the literature on other rock samples and the values calculated from standard equations for minerals and oxides. Good agreement is found for all rock systems examined. The specific heat of the four USGS silicate rock standards (in the form of fine powders) have been measured using a differential scanning calorimeter; the procedures are described by Hemingway et al. (1984). The results are listed in Table 1. Smoothed values of the specific heat (in J/g) for these rock standards may be calculated from the equations given in Table 2. The samples and the chemical compositions are described by Flanagan (1967). Sample G-2 is Westerly granite from Bradford, RI, AGV-1 is andesite from Lake County, OR, PCC-1 is peridotite from Sonoma County, CA, and BCR-1 is basalt from the Columbia River Group, WA and OR. Small amounts of H20 (presumably adsorbed on the powder) were lost from each sample during the measurements. At temperatures above about 650 K, sample PCC-1 lost significant H20, presumably the result of the breakdown of a hydrous mineral (lizardite, Flanagan, 1967). Specific-heat measurements for PCC-1 were terminated at that temperature and the measured values were extrapolated to 750 K. Measurements of the remaining three samples were extended to about 1000 K. The chemical analyses for these rocks and for other samples for which comparison calculations are made are listed in Table 3. A comparison of the measured specific heats and specific heats estimated from the modified Neumann-Kopp rule are presented in Table 4 for the four USGS rocks measured in this study. Comparisons were made using both minerals and oxides for separate estimations of specific heats. Representative values for the heat capacity and molar mass are given in Table 5 (mineral and oxide data from Robie and Hemingway, 1995) and Table 6 (values for fictive phases like crystalline H2O and CO2 ) . For Table 4, the mineral compositions of the rocks were taken from petrographic studies of the rocks given in Flanagan (1967) and Chayes (1951) and from the X-ray diffraction tests by our Survey colleague, Howard T. Evans, Jr., (written communication, 1993). The estimate based on the oxides was calculated directly from the chemical analysis. Values are given in the measurement column (Obs) for 300 K. These values are based on unconstrained extrapolations that may have significant error. At temperatures near 1000 K, the heat-capacity equations are constrained by only a few data points and thus have a larger uncertainty than the ±1% that is the norm for differential scanning calorimetric measurements. Heat-capacity values were calculated from the heat-capacity equations given in Robie et al. (1979), with the exception of H20, C02 , F2 , and silica glass (which is discussed below). Equations for the heat capacity of H2O, C02 and F2 in the crystalline phases (Table 6) in the rocks were calculated as the difference between the equations for two appropriate phases (e.g., CaCO3 CaO, as discussed above). Quartz was used in calculations based on mineral compositions where quartz was or was expected to be present, but silica glass was used in the calculations based on the oxides. This is because quartz has an a-/3 phase change and an associated heat-capacity anomaly near 844 K. A recent analysis (Richet, et al., 1982) suggests that the heat capacity for silica glass at 298.15 K that was used by Robie et al. (1979) is significantly low (about 14%). At higher temperatures the equations of the two groups are in good agreement. The results calculated in this study support the analysis of Richet et al. (1982), because the values based on the oxides and calculated from the equations of Robie et al. (1979) are anomalous at 300 K and the magnitude of the anomaly varies directly with the silica glass content. Bearing in mind these comments, the specific heat, and thus the heat content, of these rocks can be estimated to better than ± 5% using either minerals or oxides as the basis for the estimate. A review of the

Estimating heat capacity and heat content of rocks