  |
|
|
Image by Marilyn Yetzbacher |
The adiabatic constant volume calorimeter has been described in detail by Goodwin [1] and Magee[2]. A spherical bomb contains a sample of well-established mass. The volume of the bomb, approximately 73 cm3, is a function of temperature and pressure. A platinum resistance thermometer is attached to the bomb for the temperature measurement. Temperatures are reported on the ITS-90, after conversions from the original calibration on the IPTS-68. Pressures are measured with an oscillating quartz crystal pressure transducer with a 0-70 MPa range. Adiabatic conditions are ensured by a high vacuum (3x10-3 Pa) in the can surrounding the bomb, by a temperature-controlled radiation shield, and by a temperature-controlled guard ring which thermally anchors the filling capillary and the lead wires to the bomb.
For the heat capacity measurment, a precisely determined electrical energy (Q) is applied and the resulting temperature rise (DT = T2 - T1) is measured. We obtain the heat capacity from
where U is the internal energy, Q0 is the energy required to heat the empty calorimeter, Wpv is the change-of-volume work due to the slight dilation of the bomb, and n is the number of moles enclosed in the bomb. In this work, the bomb was charged with sample up to the (p,T) conditions of the highest-density isochore. The bomb and its contents were cooled to a starting temperature in the single-phase liquid region. Then, measurements were performed in that region with increasing temperature until either the upper temperature (345 K) or pressure limit (35 MPa) was attained. After the bomb was cooled with the sample down to a temperature near the triple point, measurements were begun in the two-phase region and continued into the single-phase region, up to the same limits. At the completion of a run, a small part of the sample was cryopumped into a lightweight cylinder for weighing. The next run was started with a smaller density. A maximum of four runs were measured with one filling of the bomb. When the runs were completed, the remaining sample was discharged and weighed.
Uncertainty in Cv arises from several sources. Primarily, the accuracy of this method is limited by the uncertainty of the temperature rise measurement and the change-of-volume work adjustment. In the following dicsussion, we have adopted a definition for the expanded uncertainty which is ± 2s, or two times the standard uncertainty. In other words, the expanded uncertainty has a coverage factor of 2. When we discuss uncertainties in this context, we mean this definition of expanded uncertainty at the two-sigma level.
Different sources, including calibration of the platinum resistance thermometer, radiation to or from the thermometer head, and drift of the ice point resistance, contribute to an expanded uncertainty of st = ±0.01 K at 100 K to ±0.3 K at 345 K for the absolute temperature measurement. Uncertainty of the temperature rise, however, also depends on the reproducibility of temperature measurements. The temperatures assigned to the beginning (T1) and to the end (T2) of a heating interval are determined by extrapolation of a linear temperature drift (approximately -1.0 x 10-3 to 0.5 x 10-3 K·min-1) to the midpoint time of the interval. This procedure leads to an uncertainty of ±0.001 to ±0.004 K for the extrapolated temperatures T1 and T2, depending on the standard deviation of the linear function correlated. In all cases, values from ±0.002 to ±0.006 K were obtained for the uncertainty of the temperature rise, DT = T2 - T1. For a typical experimental value of DT = 4K, this corresponds to an uncertainty of ±0.05 to ±0.15%.
The uncertainty of the change-of-volume work influences primarily the single-phase values since two-phase experiments are performed over a small pressure interval. Typically, the ratio of change-of-volume work to total applied heat ranges from 0.01 to 0.06. Estimated uncertainties of ±2.3 to ±3.0% in the change-of-volume work are due to both the deviation of the calculated pressure derivatives and the uncertainty of the volume change. This leads to an uncertainty of ±0.2% in Cv for the lowest density isochore up to ±0.3% for the highest density.
The energy applied to the calorimeter is the integral of the product of voltage and current from the initial to the final heating time. Voltage and current are measured twenty times during a heating interval. The measurements of the electrical quantities are accurate within approximately ±0.01%. However, we must account for the effect of radiation heat losses or gains which occur when a time-dependent lag of the controller leads to a small temperature difference of about 20 mK between bomb and radiation shield at the beginning and end of a heating period. Since heat transfer by radiation is proportional to T14 - T24 = 4T 3DT we would expect radiation losses to substantially increase with the bomb temperature. Therefore, the uncertainty in the applied heat is estimated to be ±0.02% for lower temperatures and up to ±0.10% for the highest temperatures. This leads to an uncertainty between ±0.04% and ±0.20% in Cv.
Other sources of uncertainty are smaller. The energy applied to the empty calorimeter has been measured in repeated experiments and fitted to a function of temperature [2]; its uncertainty is less than ±0.02%. Its influence on the uncertainty of the heat capacity is reduced, because the ratio of the heat applied to the empty calorimeter to the total heat varies only from 0.45 to 0.51 for the single-phase runs and from 0.36 to 0.42 for the two-phase runs. The mass of each sample was determined within ±0.01% by differential weighings before and after trapping the sample. The density calculated from this mass and the bomb volume has an uncertainty of approximately ±0.2%. For pressures, the uncertainty of the gauge of ±7kPa is added to the cross term for the pressure derivative in the change-of-volume work adjustment. However, neither the uncertainty of p nor r contributes appreciably to the combined uncertainty for molar heat capacity. the expanded uncertainty of Cv is estimated to be 0.7%, by combining the various sources of experimental uncertianty using a root-sum-of-squares formula; for Cv(2) it is 0.5%, and for Cs it is 0.7%.
Home |
Staff |
Instruments |
Site Index |
|
|
 |
 |
 |
Physical & Chemical Properties Division |
Chemical Science & Technology Laboratory |
NIST Boulder Labs |
NIST Homepage |
