Experimental study of the isochoric heat capacity of tert-butanol in the critical and supercritical regions

doi:10.1016/j.fluid.2011.07.004

Fluid Phase Equilibria

Volume 309, Issue 2, 25 October 2011, Pages 128-144

https://doi.org/10.1016/j.fluid.2011.07.004 Get rights and content

Abstract

The one- and two-phase isochoric heat capacities (C_V) of tert-butanol in the critical and supercritical regions have been measured with a high-temperature and high-pressure nearly constant-volume adiabatic calorimeter. The measurements were made in the temperature range from 296 K to 524 K for 21 liquid and 7 vapor isochores from 70.56 kg m⁻³ to 763.98 kg m⁻³. The isochoric heat capacity jump (quasi-static thermograms supplemented by the sensor of adiabatic control) technique was used to accurately measure of the phase transition parameters (ρ_S, T_S) in the critical region. The total experimental uncertainty of density (ρ_S), temperature (T_S), and isochoric heat capacity (C_V) measurements were estimated to be 0.02%, 15 mK, and 2–3%, respectively. The critical temperature (T_C = 506.35 ± 0.2 K) and the critical density (ρ_C = 268.1 ± 2 kg m⁻³) for tret-butanol were extracted from the measured saturated properties (C_VS, T_S, ρ_S) near the critical point. The measured C_V and saturated density (ρ_S, T_S) data near the critical point have been analyzed and interpreted in terms of extended scaling equations for the selected thermodynamic paths (critical isochore and coexistence curve) to accurately calculate the values of the asymptotical critical amplitude ( $A_{0}^{\pm}$ and B₀). The experimentally derived value of the critical amplitude ratio $A_{0}^{+} / A_{0}^{-} = 0.525$ is in good agreement with the value predicted by various scaling theories. The measured thermodynamic properties of tert-butanol near the critical point were also interpreted in terms of the “complete scaling” theory of critical phenomena. In particularly, the contributions of the “complete” and “incomplete scaling” terms on the coexistence-curve singular diameter were estimated. The Yang–Yang anomaly of strength parameter R_μ = −0.036 for tert-butanol was estimated using derived second temperature derivatives of pressure and chemical potential. The measured values of saturated one- $({C^{'}}_{V 1} and {C^{″}}_{V 1})$ and two-phase $({C^{'}}_{V 2} and {C^{″}}_{V 2})$ liquid and vapor isochoric heat capacities and saturated thermal properties (ρ_S, T_S) together with reported vapor–pressure (P_S, T_S) data were used to calculate other derived thermodynamic properties such as K_T, ΔH_vap, C_P, C_S, W, ${(\partial P / \partial T)^{'}}_{V}$ , ${(\partial V / \partial T)^{'}}_{P}$ , (d²P_S/dT²), and (d²μ/dT²) of tert-butanol at saturation near the critical point.

Highlights

► The results of C_V measurements for tert-butanol in the critical region were presented. ► The results were interpreted in terms of “incomplete” and “complete scaling” theory of critical phenomena. ► We found that singularity of the coexistence curve diameter shared by divergence of “complete” and “incomplete scaling” terms.

Introduction

In continuation of previous works on isochoric heat capacity [1], [2], [3], [4], [5], [6], [7] of hydrogen-bonded liquids such as methanol, ethanol, 1-propanol, 2-propanol, 1-butanol, 2-butanol, 1-hexanol, 1-heptanol, and 1-octanol, a study has been made of the tert-butanol (including saturation properties, ρ_S, T_S). A survey of the literature reveals that measurements of the thermodynamic properties of tert-butanol are very scarce. No previously reported C_VVT and saturation properties data on tert-butanol near the critical point. The main objective of the paper is to provide accurate isochoric heat-capacity data in the two- and one-phase regions near the critical point including coexistence curve $({C^{'}}_{V 1}, {C^{'}}_{V 2}, {C^{″}}_{V 1}, {C^{″}}_{V 2})$ , saturation liquid $({ρ^{'}}_{S})$ and vapor $({ρ^{″}}_{S})$ densities, and critical parameters (T_C, ρ_C) for tert-butanol. We also provided comprehensive analysis of the available experimental critical and saturated property data and correlations for tert-butanol to estimate the reliability and consistency of the published datasets.

Ambrose and Townsend [8] reported vapor pressure data for tert-butanol (purity of 99.96 mass%) in the temperature range from 376.42 K to 506.15 K using vertical glass tube connected with an oil-operated, dead-weight piston-gauge via a mercury-filled U tube. The sample was confined over mercury, and position of the sample-mercury interface was determined accurately by means of a cathetometer. Uncertainty of the vapor pressure measurements is 0.004 atm. The measured vapor pressures were fitted to equation $\log P_{S} = A^{'} - \frac{B}{(C + t)} - D t + E (t - F) {}^{3}, at t > 375.15 K$ and $\log P_{S} = A - \frac{B}{(C + t)}, at t < 375.15 K,$ where A = 4.32536; B = 1094.341; C = 170.658; D = 0.00026; E = 2.095 × 10⁸, and A′ = 4.35499. The vapor pressure equation determined by Krone and Johnson [9] from experimental data was as $\ln P_{S} = 39.7545 - \frac{10456}{T} - 3.215 \ln T$ Krone and Johnson [9] used the literature C_P data [10], [11] and own vapor–pressure and PVT measurements for tert-butanol to calculate derived thermodynamic properties at saturation (saturation vapor and liquid densities, enthalpies, and entropies).

Ambrose and Townsend [8] used the same apparatus to measure orthobaric density (sealed tube technique). They used 15 cm long glass tube. The derived orthobaric densities were fitted to equations ${ρ^{'}}_{S} + {ρ^{″}}_{S} = 2 ρ_{C} + a (t_{C} - t) - b {(t_{C} - t)}^{2},$ ${ρ^{'}}_{S} - {ρ^{″}}_{S} = c {(t_{C} - t)}^{1 / 3} - d {(t_{C} - t)}^{2},$ where a = 0.00132; b = 0.8 × 10⁶; c = 0.1308; d = 0.96 × 10⁶.

Costello and Bowden [12] measured saturated liquid and vapor densities for series alcohols over ranges of temperature below and above the boiling point (from 313 K to 413 K for tert-butanol). Measurements were made with a sealed dilatometer. No uncertainty of the measured densities was provided by the authors. They showed that the variation of orthobaric density difference, $({ρ^{'}}_{S} - {ρ^{″}}_{S})$ , with temperature may be represented by the equation ${ρ^{'}}_{S} - {ρ^{″}}_{S} = d_{0} {(1 - \frac{T}{T_{C}})}^{m},$ where m = 0.231 and d₀ = 0.9376 at temperatures from 313 K to 353 K; m = 0.213 and d₀ = 0.9508 at temperatures from 353 K to 413 K; and m = 0.218 and d₀ = 0.9590 at temperatures from 313 K to 413 K. Dannhauser and Bahe [13] reported saturated liquid densities of tert-butanol from 300 K to 500 K. Measurements were made with dilatometers which were constructed from precision-bore capillary tubing with a thick wall bulb blown on one end. The dilatometers were suspended in a mechanical convection oven and thermocouples, taped to the stem near the bulb, were used to monitor the temperature. No uncertainty of the measured densities was provided by the authors. Owen et al. [14] reported saturated liquid densities of tert-butanol at temperatures from 298 K to 338 K. The authors are not provided the method and uncertainty of the density measurements. Kuss [15] has measured the saturated liquid densities of tert-butanol at temperatures from 293 K to 323 K. Low temperature (below 313 K) measurements of saturated liquid densities were done by several authors [16], [17], [18]. This range is not overlap with the present temperature range. Three data points for the saturation liquid densities were reported by Smyth and Dornte [19] at temperatures from 303 K to 343 K. Only three datasets reported by Ambrose and Townsend [8], Krone and Johnson [9] (derived values), and Costello and Bowden [12] are available in the literature for the saturated vapor densities in the temperature range from 313 K to 480 K.

Saturated-vapor densities can be calculated using second virial coefficient data [20] and vapor pressures data by Ambrose and Townsend [8] as ${ρ^{″}}_{S} (T) = - \frac{0.5}{B} - {(\frac{0.25}{B^{2}} + \frac{P_{S}}{B R T})}^{1 / 2},$ where experimental second virial coefficients reported by Cox [20] were fitted to the equation $B = 54.4804 - \frac{2.904513 \times 10^{4}}{T} + \frac{522.2542865 \times 10^{6}}{T^{3}}$ In Eq. (8) T in K and B in cm³ g⁻¹. These equations, (7), (8), were use do calculate saturated-vapor densities for tert-butanol at low temperatures (below 323 K).

Krone and Johnson [9] developed Beattie–Bridgeman type equation of state for tert-butanol $P = \frac{R T}{v^{2}} (1 - \frac{c}{v T^{3}}) [v + B_{0} (1 - \frac{b}{v})] - (\frac{A_{0}}{v^{2}}) (1 - \frac{a}{v})$ where a = 0.145; A₀ = 20; b = 0.081; B₀ = 0.070; and c = 3 × 10⁷.

Very restricted (only three) critical parameter datasets are available for tert-butanol (see Table 1). Ambrose and Townsend [8] measured the critical temperature, the critical density, and the critical pressure of the tert-butanol sample using visual method (observation of the disappearance and reappearance of the meniscus). They recommended the following values of the critical parameters for tert-butanol: T_C = 506.215 K, P_C = 3.972 MPa, and ρ_C = 270.00 kg m⁻³. The derived value of the critical temperature is mean value of a series of observations on the disappearance and reappearance of the meniscus. Taking all factors into account, the authors claimed uncertainty of the critical temperature measurements is 0.2 K. The value of the critical temperature for tert-butanol was obtained from different tubes. The value of the critical pressure was measured several times with more than one filling of the experimental tube. The uncertainty of the critical pressure measurement is 0.1%. The critical density was obtained by extrapolation of the rectilinear diameter to the critical temperature, although that the rectilinear diameter is in fact curved, and the extrapolation may be subject to considerable personal variation (see below Section 5). Krone and Johnson [9] also used critical disappearance meniscus and opalescence technique to measure of the critical temperature of tert-butanol (purity was 99.8 mol%). The derived values of the critical temperature is T_C = 508.916 K. The critical pressure P_C = 4.232 MPa was obtained by extrapolation of the vapor–pressure equation to the critical temperature. The critical density derived by Krone and Johnson [9] from saturated density data is 258.36 kg m⁻³ which lowers than Ambrose and Townsend [8] measurements by 4.5%. The value of the critical temperature T_C = 508.15 K derived by Pawlewski [21] is close to the value reported by Krone and Johnson [9], while considerable (by 1.935 K) differ from the Ambrose and Townsend [8] value.

Tert-butanol sample used in this study was supplied from Russian Academy of Sciences “Akademsnab” (Moscow, Russia). The sample purity provided by supplier was >99.94 mass%.

Section snippets

Experimental

The experimental details (physical basis and the theory of the method, the apparatus, procedures of the measurements, and the uncertainty assessment) of the isochoric heat-capacity (C_VVT) and saturated properties (T_S, ρ_S) measurements have been described in detail in our earlier series publications [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36]. Below brief information will be given.

Isochoric heat-capacity (C_VVT) measurements were performed with a

Results and discussion

Measurements of the isochoric heat capacity of tert-butanol were performed at 21 liquid and 7 vapor isochores from 70.56 kg m⁻³ to 763.98 kg m⁻³, namely: (70.96, 88.43, 109.15, 148.50, 202.59, 225.56, 244.88, 270.00, 270.35, 274.77, 297.52, 316.81, 350.06, 355.5, 404.8, 435.1, 440.0, 511.1, 514.6, 517.15, 560.1, 647.3, 667.1, 678.4, 711.4, 713.0, 715.57, and 763.98) kg m⁻³. The temperatures ranged between 296 K and 524 K. These temperatures and densities are including the critical and supercritical

Two-phase isochoric heat capacities at saturation and second temperature derivatives (d²P_S/dT²) and (d²μ/dT²) behavior near the critical point

For coexistence phase the Yang and Yang [57] relation is $\frac{C_{V 2}}{T} = - \frac{d^{2} μ}{d T^{2}} + V \frac{d^{2} P_{S}}{d T^{2}},$ where C_V2 is the two-phase isochoric heat capacity and V is the specific volume. According to Eq. (20), two-phase isochoric heat capacity C_V2 is a linear function of the specific volume V along each fixed isotherm (see Refs. [1], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36]), the slopes of which are equal to T(d²P_S/dT²), while the intercepts for V = 0 are related to −T(d²μ/dT²

Singular coexistence-curve diameter from isochoric heat-capacity measurements

As was mentioned above, the continuous heating (cooling) method of measurements of the isochoric heat capacity can be used to accurately determine phase transition temperatures for each isochore, i.e., correctly determine the coexistence curve parameters T_S and ρ_S near the critical point (see Section 2, Fig. 2), therefore provide very useful information about the qualitative behavior of the coexistence curve shape near the critical point. This is very important to correct determine the value of

Derived thermodynamic properties of tert-butanol from isochoric heat capacity measurements at saturation

As was mentioned above (see Section 2), in C_V experiment we can obtain the following information on the coexistence curve: saturation temperatures (T_S); saturation liquid $({ρ^{'}}_{S})$ and saturation vapor $({ρ^{″}}_{S})$ densities; one- and two-phase liquid $({C^{'}}_{V 1}, {C^{'}}_{V 2})$ and vapor $({C^{″}}_{V 1}, {C^{″}}_{V 2})$ isochoric heat capacities at saturation. These data $(T_{S}, {ρ^{'}}_{S}, {ρ^{″}}_{S}, {C^{'}}_{V 1}, {C^{'}}_{V 2}, {C^{″}}_{V 2})$ are very useful for accurate calculations of other thermodynamic properties of fluids at saturation [35], [69], [70], [71]. For

Conclusions

The one- and two-phase isochoric heat capacities and saturation properties such as saturated liquid $({ρ^{'}}_{S})$ and vapor $({ρ^{″}}_{S})$ densities, saturated temperatures (T_S), one- and two- phase liquid $({C^{'}}_{V 1}, {C^{'}}_{V 2})$ and vapor $({C^{″}}_{V 1}, {C^{″}}_{V 2})$ saturated heat capacities of tert-butanol near the critical point has been measured in the temperature range from 296 K to 524 K for the 21 liquid and 7 vapor isochores from 70.56 kg m⁻³ to 763.98 kg m⁻³. The second temperature derivatives of the vapor pressure, (d²P_S/dT²),

Acknowledgment

One of us, I.M. Abdulagatov thanks the Thermophysical Properties Division at the National Institute of Standards and Technology for the opportunity to work as a Guest Researcher at NIST during the course of this research.

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Citation Excerpt :
The magnitude of the thermogram slopes, (dT/dτ), changes before and after the phase- transitions are proportional to the heat capacity jump ΔCV, which diverges at the critical point as ΔCV ∝ (T − TC)−α [39,40], where α = 0.11 is the universal critical exponent of the isochoric heat capacity. This makes it easy to detect any types of phase- transitions (L-L, L-S, L-V, SV) occurring in the system near the phase- transition points (even for weak phase- transitions phenomena) [41–49]. Therefore, at the same calorimetric experiment we can accurately measure isochoric heat capacities in the one- (CV1′-liquid, CV1″-vapor,) and two-phase regions (CV2'-liquid, CV2"-vapor) and the saturated liquid (ρS′) or vapor (ρS″) densities at a given temperature at phase transition point, TS.
As part of a continuing study of the critical and supercritical phenomena in fluids and fluid mixtures, one- (C_V1) and two-phase (C_V2) isochoric heat capacities, densities (ρ_S) and phase-transition temperatures (T_S) of benzene were measured in the critical and supercritical regions. Measurements were made in the immediate vicinity of the liquid-gas phase transition and the critical points in order to accurately determine of the phase transition properties (T_S,ρ_S,C_V1, and C_V2). The measurements cover the temperature range from (347 to 616) K for 10 liquid and vapor isochores between (265 and 653) kg·m⁻³ at pressure up to 7.5 MPa. The measurements were performed using a high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter. The standard uncertainties of the density, temperature, and isochoric heat capacity, C_V, measurements are estimated to be 0.1%, 0.02 K, and 1.5%, respectively. The measured one- (C_V1) and two-phase (C_V2) isochoric heat capacities along the critical isochore and the saturated liquid (ρ_S^') and vapor (ρ_S^") densities near the critical point were used to accurately estimate the theoretically meaningful asymptotic critical amplitudes (A₀^±and B₀) and related amplitudes for other properties (Γ₀⁺, D₀, ξ₀), and their universal relations, A₀⁺/A₀⁻, A₀⁺Γ₀⁺B₀², αA₀⁺Γ₀⁺B₀⁻², D₀Γ₀⁺B₀^δ−1, $ξ_{0} {(\frac{α A_{0}^{+}}{v_{C}})}^{1 / 3}$ . Saturated liquid and vapor densities (ρ_S′, ρ_S″) together with measured two-phase C_V2 data were used to estimate the values of asymmetric parameters a₃ (complete scaling parameter) and b₂ of the coexistence curve singular diameter. Experimentally determined asymptotical critical amplitudes (A₀^±and B₀ fluid-specific parameters) were used to check and confirm the predictive capability of the universal correlation in terms of their dependence on the acentric factor ω based on the generalized corresponding states principle. The measured values of two-phase C_V2 as a function of the specific volume V along various isotherms were used to calculate second temperature derivatives of vapor pressure $\frac{d^{2} P_{S}}{d T^{2}}$ and chemical potential $\frac{d^{2} μ}{d T^{2}}$ and to estimate the value of Yang-Yang anomaly strength parameter R_μ = − 0.683 for benzene. The contributions of the vapor pressure, $C_{VP} = V_{C} T \frac{d^{2} P_{S}}{d T^{2}}$ , and the chemical potential, $C_{Vμ} = - T \frac{d^{2} μ}{d T^{2}}$ , to the measured total two-phase C_V2 were derived from the measurements.

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Experimental study of the isochoric heat capacity of tert-butanol in the critical and supercritical regions

Abstract

Highlights

Introduction

Section snippets

Experimental

Results and discussion

Two-phase isochoric heat capacities at saturation and second temperature derivatives (d2PS/dT2) and (d2μ/dT2) behavior near the critical point

Singular coexistence-curve diameter from isochoric heat-capacity measurements

Derived thermodynamic properties of tert-butanol from isochoric heat capacity measurements at saturation

Conclusions

Acknowledgment

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Fluid Phase Equilib.

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Fluid Phase Equilib.

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Physica A

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Two-phase isochoric heat capacities at saturation and second temperature derivatives (d²P_S/dT²) and (d²μ/dT²) behavior near the critical point