Volume 96, Number 6, November-December 1991 Journal of Research of the National Institute of Standards and Technology [J. Res. Nat!. Inst. Stand. Technol. 96, 725 (1991)] Molar Heat Capacity (Cv) for Saturated and Compressed Liquid and Vapor Nitrogen from 65 to 300 K at Pressures to 35 MPa Volume 96 Number 6 November-December 1991 J. W. Magee Molar heat capacities at constant vol- the Cv (fi,T) data and also show satis- ume (C,) for nitrogen have been mea- factory agreement with published heat National Institute of Standards sured with an automated adiabatic capacity data. The overall uncertainty and Technology, calorimeter. The temperatures ranged of the Cy values ranges from 2% in the Boulder, CO 80303 from 65 to 300 K, while pressures were vapor to 0.5% in the liquid. as high as 35 MPa. Calorimetric data were obtained for a total of 276 state Key words: calorimeter; heat capacity; conditions on 14 isochores. Extensive high pressure; isochorlc; liquid; mea- results which were obtained in the satu- surement; nitrogen; saturation; vapor. rated liquid region (C^^^' and C„) demonstrate the internal consistency of Accepted: August 30, 1991 Glossary ticular, the heat capacity at constant volume {Cv) is a,b,c,d,e Coefficients for Eq. (7) related to P(j^T) by: c. Molar heat capacity at constant volume a Molar heat capacity in the ideal gas state (1) C„<2> Molar heat capacity of a two-phase sample Jo a Molar heat capacity of a saturated liquid sample where C? is the ideal gas heat capacity. Conse- Vbamb Volume of the calorimeter containing sample quently, Cv measurements which cover a wide Vr, Molar volume, dm' • mol"' range of {P, p, T) states are beneficial to the devel- P Pressure, MPa opment of an accurate equation of state for the P. Vapor pressure AP Pressure rise during a heating interval substance. T Temperature, K The amount of experimental data on the calorimetric Tc Critical-point temperature properties of nitrogen is very limited. Measurements of TuT2 Temperature at start and end of heating Interval Cv are mostly confined to atmospheric pressure. Only Ar Temperature rise during a heating Interval two published works concern Cv measurements at ele- Q Calorimetric heat energy input to bomb and sample Go Calorimetric heat energy input to empty bomb vated pressure. First, Voronel et al. [1] obtained 69 N Moles of substance in the calorimeter experimental values of Cv at temperatures from 106 to P Fluid density, mol • dm"' 167 K at densities close to the critical density, with an P- Saturated liquid density emphasis on the temperature variation of Cv near the P- Chemical potential critical point (126.2 K). However, these authors give nei- ther the pressures nor the densities at which the measurements were performed. Thus, comparisons with 1. Introduction the Cv data of Voronel et al. are difficult at best. In the Accurate measurements of thermodynamic prop- only other experimental study at elevated pressures, We- erties, including heat capacity, are needed to estab- ber [2] performed measurements at temperatures from lish behavior of higher order temperature 91 to 242 K using the same calorimeter as used in this derivatives of an equation of state P(p, T). In par- work. The combined works of Voronel et al. and Weber 725 Volume 96, Number 6, November-December 1991 Journal of Research of the National Institute of Standards and Technology leave gaps in the Cv surface between the triple compare these measurements with published data point (63.15 K) and 91 K, and for temperatures and with predictions from published equations of above 242 K. state. Published experimental results for the heat ca- pacity of the saturated liquid (C„) are more avail- 2. Experimental able than those for Cv at elevated pressures. When combined, the data of Weber [2], Giauque and The apparatus in Fig. 1 has a long history dating Clayton [3], and Wiebe and Brevoort [4] range to its original construction for liquid hydrogen from 65 to 125 K. However, none of these works calorimetry. Its mechanical details remain essen- spans the entire temperature domain for saturated tially unchanged since they were described by liquid nitrogen. Thus, we cannot be certain how the Goodwin [5]. Instrumentation, however, has been various data will intercompare. In this work, the changed extensively. The older instruments were goals include extending the published data for Cv replaced with electronic versions, each equipped to temperatures as low as the triple point, and also with an IEEE-488 standard interface for two-way to near ambient temperature. A second goal is to communication with a microcomputer. The ar- measure Ca over temperatures from the vicinity of rangement of the new instruments is shown in Fig. the triple point to that of the critical point, and to 2. Access Tubes Refrigerant Tubes Outer Vacuum Tube Inner Refrigerant Tanl< Cold Ring Reflux Tube Capillary Outer Refrigerant Guard Ring Dewar Shield Cold Wall Vacuum Can Calorimeter Bomb Case Thermometer Figure 1, Details of the adiabatic calorimeter. 726 Volume 96, Number 6, November-December 1991 Journal of Research of the National Institute of Standards and Technology OSCILLATING OUAFTTZ CRYSTAL PRESSURE TRANSDUCER 1 mA POWER ELECTRONIC SUPPLY COUNTER JOWPOWER SUPPLY J)2 40WPOWER StJPPLV»4 GUARD/BOMB THERMOPILE 40 W POWER SUPPLY (13 CALORIMETER SH1ELD«)MB BOMB THERMOPILE NANOVOLT- 40WPOWER ADIABATIC METER SUPPLY1P1 SHIELD / N RELAY »2 ^ NANOVOLTMETER CURRENT REUY«4 SUPPLY VOLTMETER Figure 2. Instrumentation of tlie adiabatic calorimeter. An experimental heat capacity is the apphed Mayrath [7] from 91 to 340 K in addition to new heat (Q) corrected for the heat applied to the data from 29 to 99 K, as presented in Table 1. The empty calorimeter (Qo) per unit temperature rise combined Qo data sets were fitted to the expres- (AT) per mole (N) of substance. In terms of the sion, observed measurements, the heat capacity is given 12 QoiT)='ZCi(T2'-Ti') (3) by. C. = (Q-<2o)/(NAr). (2) 1=1 by applying a chord-fitting method to AT values The applied heat is the product of the time-aver- ranging from 0.5 to 20 K. Details will follow in a aged power and the elapsed time of heating. Mea- later section. sured power is the product of instantaneous Temperatures were measured with an auto- current and potential applied to the 100 fl heater mated circuit consisting of a 25 H encapsulated wound on the surface of the calorimeter bomb. platinum resistance thermometer calibrated on the During a heat measurement a series of five power IPTS-68 by the NIST Temperature and Pressure measurements with an accuracy of 0.01% were Division, a 10 fl standard resistor calibrated by the made at 100 s intervals. Time was determined with NIST Electricity Division, a stable (±2 ppm) elec- a microcomputer clock to a resolution of 10"* s. tronic current source, and a bank of ultralow ther- Elapsed time was computed with an accuracy of mal emf (<lxl0""' V/K) relays multiplexing a 0.001%. The heat (Qo) applied to the empty precise nanovoltmeter. Potential measurements calorimeter has been determined by several series were made with the thermometer current flowing of calorimetric experiments on a thoroughly in both forward and reverse directions. An average cleaned and evacuated sphere. These results in- thermometer resistance was calculated in order to clude those of Roder [6] from 86 to 322 K and of avoid errors from spurious emfs. It is thought that 727 Volume 96, Number 6, November-December 1991 Journal of Research of the National Institute of Standards and Technology the absolute temperatures derived this way are ac- a weighing method was used to evaluate N, the er- curate within 0.03 K and precise to ±0.002 K. ror would drop to ±0.01%. Other details will fol- During this work we reproduced the generally ac- low in a later section. cepted triple point temperature of N2 to less than The spherical bomb depicted in Fig. 1 is con- 0.002 K as a further check on the validity of this structed of Type 316 stainless steel with a wall claim. Temperature rises (AT) were established thickness of 0.15 cm and an internal volume of within 0.004 K by linear extrapolation of the pre- 72.739 cm^ at 100 K. To prepare for an isochoric heating and the post-heating temperature drift experiment, N2 was charged at a pressure of 10 data to the midpoint time of the heat cycle. MPa and at a suitable bomb temperature until the Pressure was measured with an oscillating quartz target density was obtained. Then the sample was crystal pressure transducer whose signal was fed to cooled to near 63 K with liquid Ne refrigerant, or a precise timer/counter. This instrument had a to near 80 K when liquid N2 was used. Each run range of 70 MPa and was calibrated with a piston commenced in the vapor + liquid region. The gauge. The experimental uncertainty of the heater power was set to obtain about a 4 K temper- measured pressure is estimated to be ±0.01% of ature rise during each experiment. Apparatus con- full scale at pressures above 3 MPa, or trol was then turned over to the microcomputer. A ±(0.03-0.05)% of the pressure at lower pres- Fortran program was responsible for control of the sures. Finally, the number (N) of moles of sub- cell heater. The guard and shield heaters followed stance in the calorimeter is the product of the the rise of the cell temperature using a specially calorimeter volume (Fbomb) and the molar density tuned proportional-integral-derivative algorithm (p) derived from the equation of state [8] which [10].