Journal of Research of the National Bureau of Standards

Vol. 60, No. 4, April 1958

Research Paper 2848

1. Introduction

An ideal adiabatic calorimeter may be defined as one which has no heat transfer to its environment. As commonly used for the measurement of heat capacities, an adiabatic calorimeter is one which is heated over a small temperature interval, keeping the temperature of the environment as near as possible to the temperature of the calorimeter. This type of calorimeter has been used extensively at moderate and low temperatures. However, at high temperatures, the large coefficient for heat transfer by radiation increases the difficulty of avoiding heat transfer between the calorimeter and its environment. Only a few adiabatic calorimeters have been used above 500° C and even at this temperature, an accuracy as high as 1 percent is unusual [1, 2, 3, 4]. Consequently, at the high temperatures, the "drop" method has been more commonly used for the determination of heat capacities [5]. Although the drop method can reduce uncertainties due to increased heat transfer by radiation, it has one basic limitation which prevents its universal appli

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cation. This limitation is that the method can be used only for materials which reach a thermodynamically reproducible state at the temperature of the calorimeter. With certain materials having slow transitions, this reproducible state may not be reached. The element sulfur is such a material, because it has slow transitions which make accurate measurements impossible by the drop method. The calorimeter described in this report was developed for the temperature range 30° to 500° C with the intention that it would be used first to measure the heat capacity of sulfur.

2. Principles of Design

measuring heat capacity with adiabatic calorimeters in this temperature range is believed to be the uncertainty in "heat leak" (heat transfer between the calorimeter and its environment) which results from experimental departures from the ideal adiabatic condition. Two steps are taken to approach the ideal condition. First, the heat transfer coefficient between the calorimeter and its environment is made small. Second, the temperature of the environment is kept as close as possible to the temperature of the calorimeter. This second step is much more difficult because the surfaces of the calorimeter and its environment are not isothermal, especially during a heating period. Consequently, in many calorimeters thermocouple junctions are distributed over the surfaces to "integrate" the temperature gradients and obtain mean surface temperatures. This procedure introduces difficulties because the mechanism for heat transfer may be different over the various parts of the surface. For example, a part of the calorimeter having a metallic connection to the environment may lose heat mostly by metallic conduction. Another part may loose heat primarily by radiation or conduction through gas. The amount and proportion of heat transferred by various means change with temperature or other circumstances, so that the ideal distribution of thermocouples for proper integration is difficult to achieve.

In adiabatic calorimetry, one of the best procedures is to make two types of heat capacity experiments, one with an empty calorimeter (or with a small amount of sample) and one with the calorimeter filled with the sample. The purpose of the experiments with the empty calorimeter is twofold. The first purpose is to account for the heat capacity of the empty calorimeter by taking the difference in the results of the two experiments. A second purpose, which is sometimes overlooked, is to eliminate heat leak errors and certain other errors which have the same absolute value in the two types of experiments. This procedure can be extremely useful in the elimination of the effect of some unknown heat leaks. However, the procedure does not eliminate heat leak errors which are different in the two types of experiments. Unfortunately, the very existence of the sample in the calorimeter during the heating interval makes the temperature distribution in the full calorimeter different from that in the empty calorimeter. It is therefore vital, for high accuracy, to design a calorimeter having essentially the same temperature dis

This adiabatic calorimeter was designed primarily to be accurate to 0.1 percent in measuring heat capacity up to 500° C. In order to attain this accuracy, a number of factors were considered. The evaluation of electric energy input to 0.01 percent is relatively easy with modern techniques. The use of a platinum resistance thermometer for measurement of the temperature change in the calorimeter makes possible an accuracy comparable with that of the electric energy. The largest uncertainty in

1 This work was supported in part by the Allied Chemical and Dye Corporation and American Petroleum Institute Project 48A on the "Production, Isolation, and Purification of Sulfur Compounds and Measurement of Their Properties."

2 This paper includes material from a thesis submitted by E. D. West to the University of Maryland in partial fulfillment of the requirements for the degree of Master of Science.

3 Figures in brackets indicate the literature references at the end of this paper.

tribution over its outer surface in the two types of experiments. This has been accomplished in the present calorimeter by using a series of thin silver shields as described later.

In addition to high accuracy, the calorimeter was designed to require only one person for its operation. Adiabatic calorimeters capable of 0.1 percent accuracy over a moderate temperature range usually have required at least two operators. One of these operators has had to devote most of his time to controlling and recording the various temperatures pertinent to heat leak evaluation. The present calorimeter has been designed to use automatic equipment to make it possible for one person to operate the calorimeter without difficulty. The calorimeter was also designed to incorporate a sample container which could be removed from the calorimeter with a minimum of disturbance to the electrical system. To accomplish this, the calorimeter was designed in two parts, a sample container and a shield system surrounding and attached to the sample container.

3. Calorimetric Apparatus

Figure 1 is a schematic diagram of a vertical section of the apparatus. The calorimeter, defined as that part of the apparatus where energy changes are measured, is made in two main parts: (1) a sample container C surrounded by (2) a shield system consisting of the silver ring R, to which are attached two sets of silver shields S, and L. Surrounding the calorimeter is the adiabatic jacket which consists of the silver ring R2 to which silver shields S2 and L2 are attached. Between the jacket ring R2 and the calorimeter ring R, are two ten-junction thermopiles T, which indicate the vital temperature difference between the calorimeter and its jacket. Figure 2 is a

GT

photograph of the top of the calorimeter and jacket with lids L1 and L2 removed.

Surrounding the jacket is a "guard" G whose temperature is controlled a few tenths of a degree below that of the jacket to reduce the power required in the jacket and the consequent temperature gradients. It also guards the jacket from effects of changes in ambient conditions and in the temperature gradients in the glass fiber which is used for thermal insulation of the apparatus.

3.1. The Calorimeter

An essential requirement underlying the design of the calorimeter is that the temperature distribution on its outer silver surface must be independent of the amount of material in the sample container so that the empty calorimeter experiments will properly account for the exchange of small amounts of heat with the jacket. As a practical matter, it is impor tant that the container be easily removed for filling. Consequently, the additional requirement must then be imposed on the design that the temperature distribution on the outer surface also be independent of variations in thermal contact due to differences in the way the sample container is installed. It is apparent that success in meeting these requirements will depend to a great extent on minimizing changes in temperature gradients on the container itself and between the container and ring R1. It is desirable that these gradients be small so that their changes will be small.. For control purposes, the design must meet the further requirement that the calorimeter must reach thermal equilibrium quickly.

The sample container C, figure 1, is a cylinder 2 in. high and 2 in. in diameter made from aluminum alloy 1100 (99+ percent pure) with a stainless steel cover screwed on the bottom. Aluminum was used here so that the container could later be adapted to the measurements on sulfur. In order to distribute heat quickly to the sample and keep gradients small, the

container is made from a solid cylinder of aluminum by boring many holes 2 to 5 mm in diameter and leaving a web of metal between holes so that no part of the sample is more than 2.5 mm from a good thermal conductor. The container has an internal volume of 70 cm3 and a mass of about 112 g. In a central well in the container is a platinum resistance thermometer enclosed (but not sealed) in a Vycor tube which is ground cylindrical to permit a good fit in the well. Also inserted in the top of the sample container are three coils (HIA, fig. 1) of the calorimeter heater. This placement of the heaters permits observation of the calorimeter temperature within a few hundredths of a degree while heating.

The sample container is held against the silver ring by a thin stainless steel ring and twelve stainless steel screws. To avoid contact of aluminum with silver, another thin stainless ring is silver-soldered to the ring where it is in contact with the sample container. This second stainless ring also provides a strong material for attaching the screws.

The ring R1 is made of pure silver 0.8 cm2 in cross section to reduce temperature gradients due to circumferential heat flow. It provides space for 12 short heater coils and 20 junctions of the thermopiles which measure the effective temperature difference between the calorimeter and its jacket. Silversoldered to the ring are three silver shields each 0.25 mm thick. The function of the shields is to provide an external surface on which the effect of the gradients on the sample container and between the sample container and the ring is greatly attenuated. It is calculated that the attenuation by one shield is a factor of about 8, so that the attenuation by three shields should be about 500. The temperature differences on the surface of the sample container are significant only during the heating interval. They are calculated to be not greater than 0.02° C when empty and 0.04° C when full. The temperature difference between the sample container and the ring is made small by distributing the calorimeter heater between them approximately in proportion to their heat capacities. By various combinations of the heating coils allowance is made for the full or empty sample container. During heating, the temperature difference between the sample container and the ring is calculated to be about 0.05° C, which is less than 10 percent of what it would be if the heater were all in the ring. Assuming the uncertainty in the reproducibility of this gradient is as much as the calculated gradient, the variation in the average temperature of the outer surface of the calorimeter due to variations on the sample container is estimated to be only about 0.0001° C.

More critical than the thermal contact between the container and the ring is the contact between the lid L1 and the ring R1, because variations in this contact are not attenuated and directly affect the temperature over almost one-sixth of the outer surface of the calorimeter. This contact is made between the soft silver lid screwed down against a stainless steel ring. Although the heat capacity of the lid is small, all the heat required to raise its temperature during the heating interval must come

from the heaters in the ring through this mechanical contact. In disassembling the calorimeter, this contact is usually found to be so good that the lid and ring must be forced apart, indicating that some heat is transferred by direct metal-to-metal conduction. However, to arrive at an estimate of how large the temperature difference between the ring and the lid may be, it is assumed that heat transfer is only by gaseous conduction through an effective spacing of 0.0002 in. With these assumptions, the temperature difference between lid and ring is calculated to be 0.001° C. The single-junction thermocouple T3 is not sensitive enough to determine variations in this thermal contact, but it does set an upper limit of a few thousandths of a degree.

The calorimeter heater was designed to have large electrical resistance and small heat capacity. The coils for this heater (and also for the jacket heater) are made by winding helices of oxidized 38 Nichrome V wire to fit inside porcelain tubes 1 mm i. d. The lead from the lower end of each coil is brought up through a smaller porcelain tube inside the helix. To reduce the heat developed in the leads between coils, the helices are arc welded in helium to larger nickel leads. The total resistance of all calorimeter heaters in series would be 640 ohms, but the sections are connected in two series-parallel combinations to give 77 ohms for the empty calorimeter and 60 ohms for the full calorimeter. The heat capacity of the heater is about 1 j deg-1 C, which is less than 0.3 percent of the heat capacity of the full calorimeter.

3.2. The Adiabatic Jacket

The main purpose of the adiabatic jacket is to minimize heat transfer from the calorimeter. To accomplish this purpose, both the heat transfer coefficient and the temperature difference between the jacket and the calorimeter are made small. The jacket is adiabatic if its effective temperature is equal to that of the calorimeter. At equilibrium, this equality can be checked by following the calorimeter temperature. However, during the heating interval, no such check on the heat transfer is available. In place of effective temperature equality, the more feasible requirement has been substituted that temperature inequalities and the corresponding small heat losses be the same in the two experiments-one with the calorimeter full and one with it empty. If this substitute requirement is satisfied, then, when the empty heat capacity is subtracted from the full heat capacity, allowance is automatically made for those small heat losses which are the same in the two types of experiments. The uncertainty in the equality of these small heat losses is frequently the chief limitation on the accuracy of the heat capacity measurements.

In order that heat losses compensate, any errors in measuring the temperature difference between the calorimeter and its jacket must be the same in the two types of experiments. These errors are greatest during the heating interval. To make them the same in the empty and full experiments, the thermopile junctions must have the same thermal lags and the gradients on the outer surface of the calorimeter

and the inner surface of the jacket must be the same. The temperature difference between the jacket ring and the calorimeter ring is measured by means of two ten-junction Chromel-Alumel thermopiles (T1, fig. 1) connected so that their emf's are additive. These two thermopiles are compared frequently by opposing their emf's to detect circumferential gradients on the silver rings. The junctions are made at "thermal tiedowns" which consist of small gold tabs sandwiched between mica washers for electric insulation and squeezed against the silver rings by stainless steel nuts. These thermal tiedowns are similar to, but larger than, those used previously in this laboratory [6]. At the usual heating rate of 0.5° C min-1, tests indicate the junctions of the thermopile lag about 0.02° C below the rings. The lag in junctions on the calorimeter is compensated for by the lag in those on the jacket, so that the error in the observed temperature difference will be considerably less than 0.02° C. However, it is necessary to have this temperature difference reproducible to better than 0.001° C between the full and empty measurements. To insure maximum reproducibility, the thermopile junctions are not disturbed when the sample container is removed for filling. To prevent cooling of the thermopile junctions by conduction along the leads an extra thermal tiedown was installed in each of the four leads to bring them to the jacket tempera

ture.

In addition to making the thermal lags the same, the gradients on the inner shield of the jacket must be reproducible, just as the gradients on the outer surface of the calorimeter must be reproducible. However, the variations to be attenuated by the jacket are due to disturbances on the outside and are considerably larger. The attenuation at 400° C has been determined by altering the guard temperature 0.75° C and observing the effect on the calorimeter. The change in the rate of heat transfer corresponds to an offset of the jacket temperature of 0.0056° C, an attenuation of 130. The attenuation is much greater at lower temperatures. The uncertainty in the guard temperature, estimated from observations of time and circumferential variations of thermocouples is less than 0.3° C. From this estimate the uncertainty in reproducing the temperature distribution inside the jacket is calculated to be

about 0.002° to 400° C.

During the heating period, there are gradients on the shields S1 and S2 due to heat flowing from the rings R and R2 to raise the temperature of the shields. When the calorimeter is being heated at 0.5° C min-1, the temperature difference between the ring and the center of the bottom of the corresponding shield is about 0.1° C. The maximum temperature difference between the outer shield of the calorimeter and the inner shield of the jacket occurs between the centers of the shield bottoms and is about 0.05° C. The gradients in these two shields and therefore the effective temperature difference between them are very nearly proportional to the rate of heating. Consequently, the rate at which heat is lost from the calorimeter by transfer between these shields is directly proportional to the rate of

heating. On first thought, it may appear that the rate of heating in the empty experiment would have to be made the same as in the full experiment. That this is not the case may be seen from the following considerations: In any given experiment, the heating rate is virtually constant, so that energy lost from the calorimeter is directly proportional to the product of the heating rate and the time of heating. Since this product is equal to the change in the calorimeter temperature, the energy lost is the same in the empty and full experiments if they have the same initial and final temperatures. The rate of heating in both full and empty experiments was adjusted to 0.5° C min-1 within 3 percent, but, to establish the validity of the above conclusion, two experiments in which the heating rate was one-half the usual rate were carried out at 660.05 and 669.75° K. The data for these two experiments are given in table, 1 (see note b). At these temperatures the large heat transfer coefficient would result in the largest effect on the heat capacity values, but no such effect is apparent.

In addition to reproducing the errors in measuring the temperature difference, it is necessary to avoid changes in the heat transfer coefficient between the empty and full experiments. During the heating interval, the gradient on the inner jacket shield is different from that on the outer calorimeter shield, resulting in a net temperature difference even when the ring temperatures are matched. If the heat transfer coefficient were to change between the empty and full measurements, there would be a systematic error equal to the product of this change and the average temperature difference between the shields, which is calculated to be about 0.026° C at the normal heating rate.

To avoid large absolute changes in the heat transfer coefficient, it has been made small by using silver for the outer surfaces of the calorimeter and the inner surfaces of the jacket. The silver surfaces were clean, but not polished. Silver loses its polish when heated, but the heat transfer by radiation is not changed much because the orientations of the new crystallite faces are at small angles with the average plane of the surface. The coefficient for heat transfer by radiation is calculated to be 0.10 w deg-1 C at 400° C. The coefficient for heat transfer by CO2 gas conduction across the 1-cm space is calculated to be 0.07 w deg1 C at 400° C. Although the heat transfer coefficient could be reduced by the amount of the gas conduction if the system were evacuated, the gain would be more than offset by the adverse effects where good thermal contact is desired, i. e., at the lids, heaters, thermocouple junctions and the thermometer.

Heat conduction along leads and supports is minimized by using small wires and poor conductors whenever possible. The thermopile is made__ of No. 36 AWG Chromel P and Alumel wires. The seven heater and thermometer leads are No. 32 AWG gold between the calorimeter and the jacket. The three supports for the calorimeter are Nichrome V, 6 mm wide and 0.1 mm thick. The total metallic conductance is about 0.006 w deg1 C. The leads

are brought to the temperature of the rings by the same tiedown technique used for the thermopile junctions. The leads and supports are not disturbed when the container is removed. Calculations indicate that heat transfer by convection is wholly negligible, so that the over-all heat transfer coefficient for flow from the calorimeter is calculated to be about 0.18 w deg-1 C at 400° C.

By controlling the jacket temperature about 0.01° C hot or cold, the change in heat flow from the calorimeter leads to an experimental evaluation of the heat transfer coefficient. At 400° C, the mean value of this coefficient is 0.23 w deg-1 C, with a standard deviation of ±0.02 which is in reasonable agreement with the calculated value above. Estimating the average uncertainty in the temperature difference from all causes to be 0.001° C at 400 and considering a typical 40-min experiment, the

heat loss due to this heat loss due to this uncertainty is equivalent to 0.08 percent of the heat capacity of the Al2O3. This 0.08-percent uncertainty is comparable to the scatter of the heat capacity results around 670° K (table 1). This considerable heat effect from such a small temperature difference is indicative of the difficulties of adiabatic calorimetry at elevated temperatures.

3.3. Guard System

The guard G is made from aluminum 2 cm thick. The heaters are in three sections distributed over the surface. The guard temperature is automatically controlled about 0.3° C below the jacket temperature using a single junction Chromel-Alumel thermocouple between the jacket ring and the cylindrical section of the guard. This temperature difference permits