Calorimeter, flow heat-capacity

Figure 6-17 illustrates a constant-volume calorimeter of a type that is often used to measure q for combustion reactions. A sample of the substance to be burned is placed inside the sealed calorimeter in the presence of excess oxygen gas. When the sample bums, energy flows from the chemicals to the calorimeter. As in a constant-pressure calorimeter, the calorimeter is well insulated from its surroundings, so all the heat released by the chemicals is absorbed by the calorimeter. The temperature change of the calorimeter, with the calorimeter s heat capacity, gives the amount of heat released in the reaction. 

Figure 5. Schematic of flow, heat-capacity calorimeter...

A CONTINUOUS-FLOW HEAT-CAPACITY CALORIMETER. M.S. THESIS. 

Hnedkovsky, L, Hynek, V., Majer, V., and Wood, R.H. (2002) A new version of difierential flow heat capacity calorimeter tests of heat loss corrections and heat capacities of aqueous NaCl from T = 300 K to T= 623 K. /. Chem. Thermodyn., 34, 755-782. 

The heat capacity of a gas at constant pressure is nonually detenuined in a flow calorimeter. The temperature rise is detenuined for a known power supplied to a gas flowing at a known rate. For gases at pressures greater than about 5 MPa Magee et al [13] have recently described a twin-bomb adiabatic calorimeter to measure Cy. 

Solution calorimetry covers the measurement of the energy changes that occur when a compound or a mixture (solid, liquid or gas) is mixed, dissolved or adsorbed in a solvent or a solution. In addition it includes the measurement of the heat capacity of the resultant solution. Solution calorimeters are usually subdivided by the method in which the components are mixed, namely, batch, titration and flow. 

Various flow calorimeters are available connnercially. Flow calorimeters have been used to measure heat capacities, enthalpies of mixing of liquids, enthalpy of solution of gases in liquids and reaction enthalpies. Detailed descriptions of a variety of flow calorimeters are given in Solution Calorimetry by Grolier [17], by Albert and Archer [18], by Ott and Womiald [H], by Simonson and Mesmer [24] and by Wadso [25]. 

To measure the heat flow in a reaction, a device known as a calorimeter is used. The apparatus contains water and/or other materials of known heat capacity. The walls of the calorimeter are insulated so that there is no exchange of heat with the surrounding air. It follows that the only heat flow is between the reaction system and the calorimeter. The heat flow for the reaction system is equal in magnitude but opposite in sign to that of the calorimeter ... 

Bomb calorimeter. The heat flow, q, for the reaction is calculated from the temperature change multiplied by the heat capacity of the calorimeter, which is determined in a preliminary experiment... 

Knowing the heat capacity of the calorimeter, the heat flow for any reaction taking place within the calorimeter can be calculated (Example 8.3). 

When heat is liberated or absorbed in the calorimeter vessel, a thermal flux is established in the heat conductor and heat flows until the thermal equilibrium of the calorimetric system is restored. The heat capacity of the surrounding medium (heat sink) is supposed to be infinitely large and its temperature is not modified by the amount of heat flowing in or out. The quantity of heat flowing along the heat conductor is evaluated, as a function of time, from the intensity of a physical modification produced in the conductor by the heat flux. Usually, the temperature difference 0 between the ends of the conductor is measured. Since heat is transferred by conduction along the heat conductor, calorimeters of this type are often also named conduction calorimeters (20a). 

The Petit-Eyraud apparatus is a differential calorimeter but it is not a twin calorimeter. The reference cell serves also as a heat sink of limited heat capacity, since it collects, at least transiently, the heat flowing along... 

The value of the time constant depends upon the calorimeter itself p and upon the heat capacity of the calorimeter cell and of its contents p. Typical, but necessarily approximate, values of the time constant for some heat-flow microcalorimeters are given in Table II. 

It must be noted that the heat capacity of the calorimeter cell and of its contents p, which appears in the second term of Tian s equation [Eq. (12)], disappears from the final expression giving the total heat [Eq. (19)]. This simply means that all the heat produced in the calorimeter cell must eventually be evacuated to the heat sink, whatever the heat capacity of the inner cell may be. Changes of the heat capacity of the inner cell or of its contents influence the shape of the thermogram but not the area limited by the thermogram. It is for this reason that heat-flow microcalorimeters, with a high sensitivity, are particularly convenient for investigating adsorption processes at the surface of poor heat-conducting solids similar in this respect to most industrial catalysts. 

As already indicated, Tian s equation supposes (1) that the temperature of the external boundary of the thermoelectric element 8e, and consequently of the heat sink, remains constant and (2) that the temperature Oi of the inner cell is uniform at all times. The first condition is reasonably well satisfied when the heat capacity of the heat sink is large and when the rate of the heat flux is small enough to avoid the accumulation of heat at the external boundary. The second condition, however, is physically impossible to satisfy since any heat evolution necessarily produces heat flows and temperature gradients. It is only in the case of slow thermal phenomena that the second condition underlying Tian s equation is approximately valid, i.e., that temperature gradients within the inner cell are low enough to be neglected. The evolution of many thermal phenomena is indeed slow with respect to the time constant of heat-flow calorimeters (Table II) and, in numerous cases, it has been shown that the Tian equation is valid (16). 

A marginal but very important application of the drop calorimetric method is that it also allows enthalpies of vaporization or sublimation [162,169] to be determined with very small samples. The procedure is similar to that described for the calibration with iodine—which indeed is a sublimation experiment. Other methods to determine vaporization or sublimation enthalpies using heat flow calorimeters have been described [170-172], Although they may provide more accurate data, the drop method is often preferred due to the simplicity of the experimental procedure and to the inexpensive additional hardware required. The drop method can also be used to measure heat capacities of solids or liquids above ambient temperature [1,173],... 

The heat flux and energy calibrations are usually performed using electrically generated heat or reference substances with well-established heat capacities (in the case of k ) or enthalpies of phase transition (in the case of kg). Because kd, and kg are complex and generally unknown functions of various parameters, such as the heating rate, the calibration experiment should be as similar as possible to the main experiment. Very detailed recommendations for a correct calibration of differential scanning calorimeters in terms of heat flow and energy have been published in the literature [254,258-260,269]. 

The isothermal and isoperibol calorimeters are well suited to measuring heat contents from which heat capacities may be subsequently derived, while the adiabatic and heat-flow calorimeters are best suited to the direct measurement of heat capacities and enthalpies of transformation. 

Handa, Y.P. (1986a). Compositions, enthalpies of dissociation, and heat capacities in the range 85 to 270 K for clathrate hydrates of methane, ethane, and propane, and enthalpy of dissociation of isobutane hydrate, as determined by a heat-flow calorimeter. J. Chem. Thermodynamics, 18 (10), 915-921. 

A common variety of constant-volume calorimetry is bomb calorimetry, a technique in which a reaction (often, a combustion reaction) is triggered within a sealed vessel called a bomb. The vessel is immersed in a water bath of known volume. The temperature of the water is measured before and after the reaction. Because the heat capacity of the water and the calorimeter are known, you can calculate heat flow from the change in temperature. 

Standard heat capacities of transfer can be derived from the temperature dependence of standard enthalpies of solution (8). While this technique can give general trends in the transfer functions from water to mixed solvents (9), it is not always sufficiently precise to detect the differences between similar cosolvents, and the technique is rather laborious. Direct measurements of the difference between heat capacities per unit volume of a solution and of the solvent a — gq can be obtained with a flow microcalorimeter (10) to 7 X 10 5 JK 1 cm-3 on samples of the order of 10 cm3. A commercial version of this instrument (Picker dynamic flow calorimeter, Techneurop Inc.) has a sensitivity improved by a factor oi about two. 

The heat capacity of skim milk has been carefully measured by Phipps (1957), who compared his results with those of earlier workers. Skim milk exhibits a small but definite linear increase in heat capacity between 1 and 50°C from about 0.933 to 0.954 cal g 1C 1. Bertsch (1982) used a continuous-flow calorimeter to measure heat capacities at temperatures up to 80 °C. Since the total time in the calorimeter was 10 sec, the values of 0.968 (skim) and 0.939 cal g 1C 1 (whole milk) at... 

Other calorimeters include heat-leak calorimeters", such as of Thomas Parks (Ref 25,p 545), "automatic calorimeters such as of Andrews, Berl Stull (Ref 25,p 551) "vacum-walled calorimeter (Ref 3,p 153) "aneriod (unstirred) calorimeters" (Ref 3,pp 23,160-7), "rotating bomb calorimeters", such as of Popov, Shirokikh and of Hubbard (Ref 25,p 594) liquid-phase calorimeter" of Kistiakowsky (Ref 25,p 636), "gas calorimeter of Cutler- Hammer (Ref 18a), calorimeter for gaseous heat capacities of Waddington (Ref 15,p 802), "flow calorimeter of Junkers (Ref 15,p 805)," flow calorimeter of Osborne et al (Ref 25,p 565), "flow calorimeter of Pitzer (Ref 25,p 566), "flow calorimeter of Bennewitz Schulze (Ref 25,p 567) and "fiame calorimeter of Rossini" (Ref 25,pp 600--2). An apparatus for detn of heats of vaporization is described in Ref 25,p 615 and an "adsorption calorimeter in Ref 25,p 618... 

In the CSM laboratory, Rueff et al. (1988) used a Perkin-Elmer differential scanning calorimeter (DSC-2), with sample containers modified for high pressure, to obtain methane hydrate heat capacity (245-259 K) and heat of dissociation (285 K), which were accurate to within 20%. Rueff (1985) was able to analyze his data to account for the portion of the sample that was ice, in an extension of work done earlier (Rueff and Sloan, 1985) to measure the thermal properties of hydrates in sediments. At Rice University, Lievois (1987) developed a twin-cell heat flux calorimeter and made AH measurements at 278.15 and 283.15 K to within 2.6%. More recently, at CSM a method was developed using the Setaram high pressure (heat-flux) micro-DSC VII (Gupta, 2007) to determine the heat capacity and heats of dissociation of methane hydrate at 277-283 K and at pressures of 5-20 MPa to within 2%. See Section 6.3.2 for gas hydrate heat capacity and heats of dissociation data. Figure 6.6 shows a schematic of the heat flux DSC system. In heat flux DSC, the heat flow necessary to achieve a zero temperature difference between the reference and sample cells is measured through the thermocouples linked to each of the cells. For more details on the principles of calorimetry the reader is referred to Hohne et al. (2003) and Brown (1998). 

---