Thermophysical Properties of 1-Butanol at High Pressures †

1-Butanol can be considered as a good fuel additive, which can be used at high pressures. Therefore, the knowledge of high-pressure thermophysical properties is crucial for this application. In this paper, new experimental data on the speed of sound in 1-butanol in the temperature range from 293 to 318 K and at pressures up to 101 MPa are reported. The speed of sound at a frequency of 2 MHz was measured at atmospheric and high pressures using two measuring sets operating on the principle of the pulse–echo–overlap method. The measurement uncertainties were estimated to be better than ±0.5 m·s−1 and ± 1 m·s−1 at atmospheric and high pressures, respectively. Additionally, the density was measured under atmospheric pressure in the temperature range from 293 to 318 K using a vibrating tube densimeter Anton Paar DMA 5000. Using the experimental results, the density and isobaric and isochoric heat capacities, isentropic and isothermal compressibilities, isobaric thermal expansion, and internal pressure were calculated at temperatures from 293 to 318 K and at pressures up to 100 MPa.


Introduction
1-Butanol is an important chemical platform used as feedstock in the plastic industry, plasticizers, paints, binders and food extractant. However, much attention has been paid to the use of 1-butanol as a fuel. 1-Butanol can be used as an additive for gasoline, diesel, and kerosene or as an alternative fuel [1][2][3][4]. Studies show that the use of 1-butanol for this purpose is much more advantageous than the use of ethanol. 1-Butanol has higher energy density, lower than ethanol vapor pressure and improved miscibility with gasoline, lower solubility in water and it is less corrosive than ethanol [2,5,6]. Currently, 1-butanol is produced almost entirely from petroleum and the global demand for 1-butanol is about 2.8 metric tons per year [1]. The International Energy Agency forecasts that the demand for biofuels will be 690 million tons per year in 2050 [1]. The strong renewed interest in 1-butanol as a sustainable vehicle fuel has led to the development of improved biobutanol production processes including both biotechnological production processes as well as separation techniques [1,[7][8][9][10][11]. Various species of the Clostridium bacteria such as C. acetobutylicum, C. beijerinckii, C. saccharoperbutylacetonicum and C. saccharobutylicum are mainly used for 1-butanol production [7]. However, Clostridium can be genetically modified in order to increase its ability to produce 1-butanol, and others have extracted enzymes from bacteria and incorporated them into other microbes such as yeast in order to turn them into 1-butanol production. Yeast (for example, Sacharomyces cerevisiae [8]) and Escherichia coli, one of the major bacteria in the human gut, are believed to be easily grown on an industrial scale [7]. The produced biobutanol can be separated by several methods including adsorption, gas stripping pervaporation, and liquid-liquid extraction using, for example, ionic liquids [6,8,11]. The next stage is the test of the properties of biobutanol in terms of its use in engines. In the injection systems used in automotive engines, the pressure can reach 250 MPa and the fuel injection takes place under Table 1. Comparison of the speed of sound, u, and density, ρ, at atmospheric pressure obtained in this work with those reported in the literature.

Speed of Sound Measurements
The speed of sound measurements were conducted at ambient and high pressures using two measuring sets operate based on the pulse-echo-overlap method with measuring vessels of the same acoustic path and constructed by a single transmitting-receiving ceramic transducer of 2 MHz and an acoustic mirror. The pressure was measured using a strain gauge measuring system (Hottinger Baldwin System P3MD) with accuracy better than 0.15%. During measurements, the pressure stability was ±0.03 MPa. The temperature was measured by an Ertco Hart 850 platinum resistance thermometer (NIST certified) with an uncertainty of ±0.05 K and resolution of 0.001 K. During measurements, the stability of temperature was ±0.005 K at ambient pressure and ±0.01 K at high pressures. The uncertainties of the speed of sound measurements under ambient and high pressures were estimated to be better than ±0.5 m·s −1 and ±1 m·s −1 , respectively. The details concerning the construction of a high-pressure device as well as the method of the speed of sound measurements and calibration can be found in the previous paper [33].

Density Measurements
The density was measured at atmospheric pressure using a vibrating tube densimeter Anton Paar DMA 5000. The calibration was conducted using the extended procedure with dry air and re-distilled water. The uncertainty of the density measurements was estimated to be ±0.05 kg·m −3 .

Results and Discussion
The speed of sound in 1-butanol was measured from (293 to 318) K in about 5 K steps and under the pressures up to 101.34 MPa. The experimental values are listed in Table 2. The relative deviations RDs between the high-pressure speed of sound obtained of this work and literature values are in the range from 0.12% [15] to −3.3% [16] (see Figure 3). Additionally, the absolute average relative deviations (AARDs) between results obtained in this work (yexp) and the literature values (ylit) were calculated as (where N is the number of data points). The AARDs equal 0.03% [14], 0.08% [15], and 1.1% [16].  [16,26,27,30] presented as relative deviations RDs (RD/% = 100·(ρ this work −ρ lit )/ρ this work ).

Speed of Sound Measurements
The speed of sound measurements were conducted at ambient and high pressures using two measuring sets operate based on the pulse-echo-overlap method with measuring vessels of the same acoustic path and constructed by a single transmitting-receiving ceramic transducer of 2 MHz and an acoustic mirror. The pressure was measured using a strain gauge measuring system (Hottinger Baldwin System P3MD) with accuracy better than 0.15%. During measurements, the pressure stability was ±0.03 MPa. The temperature was measured by an Ertco Hart 850 platinum resistance thermometer (NIST certified) with an uncertainty of ±0.05 K and resolution of 0.001 K. During measurements, the stability of temperature was ±0.005 K at ambient pressure and ±0.01 K at high pressures. The uncertainties of the speed of sound measurements under ambient and high pressures were estimated to be better than ±0.5 m·s −1 and ±1 m·s −1 , respectively. The details concerning the construction of a high-pressure device as well as the method of the speed of sound measurements and calibration can be found in the previous paper [33].

Density Measurements
The density was measured at atmospheric pressure using a vibrating tube densimeter Anton Paar DMA 5000. The calibration was conducted using the extended procedure with dry air and re-distilled water. The uncertainty of the density measurements was estimated to be ±0.05 kg·m −3 .

Results and Discussion
The speed of sound in 1-butanol was measured from (293 to 318) K in about 5 K steps and under the pressures up to 101.34 MPa. The experimental values are listed in Table 2. The relative deviations RDs between the high-pressure speed of sound obtained of this work and literature values are in the range from 0.12% [15] to −3.3% [16] (see Figure 3). Additionally, the absolute average relative deviations (AARDs) between results obtained in this work (y exp ) and the literature values (y lit ) were calculated as AARD = (100/N) n i=1 (y exp, i − y lit, i )/y exp, i (where N is the number of data points). The AARDs equal 0.03% [14], 0.08% [15], and 1.1% [16].     [14][15][16] presented as relative deviations RDs (RD/% = 100·(uthis work−ulit)/uthis work); * calculated from the pρT data [16].
The density of the alcohol under test was measured under atmospheric pressure within the temperature range from (293.15 to 318.15) K. The experimental values are collected in Table 1.
The dependence of the speed of sound and density on the temperature at atmospheric pressure was approximated by the second-order polynomial: where y is the speed of sound, u0, or density, ρ, at atmospheric pressure p0, b j are the polynomial coefficients (   [14][15][16] presented as relative deviations RDs (RD/% = 100·(u this work −u lit )/u this work ); * calculated from the pρT data [16].
The density of the alcohol under test was measured under atmospheric pressure within the temperature range from (293.15 to 318.15) K. The experimental values are collected in Table 1.
The dependence of the speed of sound and density on the temperature at atmospheric pressure was approximated by the second-order polynomial: where y is the speed of sound, u 0 , or density, ρ, at atmospheric pressure p 0 , bj are the polynomial coefficients (b j = c j for the speed of sound, and b j = ρ j for the density) calculated by the least-squares method. The backward stepwise rejection procedure was used to reduce the number of non-zero coefficients. The coefficients and standard deviations from the regression lines are provided in Table 3.  The speed of sound dependence on pressure and temperature was approximated using the equation proposed by Sun et al. [24]: where a ij are the polynomial coefficients calculated by the least-squares method, u is the speed of sound at p > 0.1 MPa, u 0 is the speed of sound at ambient pressure, calculated from Equation (1). The coefficients a ij and the mean deviation from the regression line are provided in Table 4. The stepwise rejection procedure was used to reduce the number of non-zero coefficients.  (2).
a mean deviation from the regression line.
The density and isobaric heat capacity of 1-butanol were determined for temperatures from (293 to 318) K and for pressures up to 100 MPa using the acoustic method. In the calculations, the experimental speed of sound data as a function of temperature and pressure were used, together with the temperature dependence of density and isobaric heat capacity at atmospheric pressure. The temperature dependence of the isobaric heat capacity reported by Zábranský et al. [22] was used.
The applied acoustic method is based mainly on the thermodynamic relationship between isothermal compressibility κ T and isentropic compressibility κ S : where c p is the specific isobaric heat capacity and α p is the isobaric thermal expansion defined as: The substitution the Laplace formula: and definition of isothermal compressibility: Energies 2020, 13, 5046 7 of 21 into Equation (3) leads to the following relationship: The change of density, ∆ρ, caused by the change of pressure from p 1 to p 2 at constant temperature T can be approximated sufficiently accurate as follows: provided that ∆p = p 2 -p 1 is small. The initial values of u(T, p 0 = 0.101325 MPa), ρ(T, p 0 = 0.101325 MPa), and c p (T, p 0 = 0.101325 MPa) were used in the Equation (8). The specific isobaric heat capacity at p 2 is acquired by: where c p (p 1 ) is the specific isobaric heat capacity at p 1 . The uncertainties of the density and specific isobaric heat capacity estimated using the perturbation method are ±0.02% and ±0.3%, respectively. The expanded uncertainties were estimated to be better than U(ρ) = 5·10 −4 ·ρ kg·m −3 and U(C p )=1·10 −2 ·C p J·mol −1 ·K −1 for density and molar isobaric heat capacity, respectively. The density and molar isobaric heat capacity at high pressures are collected in Tables 5 and 6, respectively.   The density of 1-butanol obtained in this work was compared with the experimental data reported by 1993, correlated by Cibulka and Ziková [19]. The RDs are in the range from 0.02 to 0.09% (see Figure 4). The AARD was found to be 0.04%. Particularly, the attention has been paid to excellent agreement between the raw density reported by Zúñiga-Moreno et al. [34] and density obtained in this work as follows: 801.97 kg·m −3 at 313.10 K, 9.996 MPa [34] and 801.98 kg·m −3 at 313.15 K, 10 MPa as well as 809.14 kg·m −3 at 313.10 K, 20.015 MPa [34] and 809.14 kg·m −3 at 313.15 K, 20 MPa. A good agreement was found also for data reported by Dávila et al. [17]. The RDs are in the range from −0.13% to −0.004% (see Figure 4), the AARD is 0.07%. The density obtained in this work is also in very good agreement with those reported by Safarov et al. [16], the RDs are in the range from −0.04 to 0.08% (see Figure 4) and AARD equals 0.04%. Thus, again the density calculated by the indirect, acoustic method is in an excellent agreement with density measured by high-pressure vibrating tube densimeter. On the other hand, the speed of sound calculated from experimental ρ(p,T) data is in worse agreement with experimental ones (see Figure 3). This was discussed in detail in the previous work [35]. Using both the acoustic method and densimetric one, the C p (p,T) data can be obtained by the same relationship (Equation (6)). The agreement between the C p (p,T) data obtained by the acoustic method (this work) and densimetric one (reported by Safarov et al. [16]) is excellent, the RDs are in the range from −0.67 to 0.17% and AARD is 0.22% (see Figure 5). The density of 1-butanol obtained in this work was compared with the experimental data reported by 1993, correlated by Cibulka and Ziková [19]. The RDs are in the range from 0.02 to 0.09% (see Figure 4). The AARD was found to be 0.04%. Particularly, the attention has been paid to excellent agreement between the raw density reported by Zúñiga-Moreno et al. [34] and density obtained in this work as follows: 801.97 kg·m −3 at 313.10 K, 9.996 MPa [34] and 801.98 kg·m −3 at 313.15 K, 10 MPa as well as 809.14 kg·m −3 at 313.10 K, 20.015 MPa [34] and 809.14 kg·m −3 at 313.15 K, 20 MPa. A good agreement was found also for data reported by Dávila et al. [17]. The RDs are in the range from −0.13% to −0.004% (see Figure 4), the AARD is 0.07%. The density obtained in this work is also in very good agreement with those reported by Safarov et al. [16], the RDs are in the range from −0.04 to 0.08% (see Figure 4) and AARD equals 0.04%. Thus, again the density calculated by the indirect, acoustic method is in an excellent agreement with density measured by high-pressure vibrating tube densimeter. On the other hand, the speed of sound calculated from experimental ρ(p,T) data is in worse agreement with experimental ones (see Figure 3). This was discussed in detail in the previous work [35]. Using both the acoustic method and densimetric one, the Cp(p,T) data can be obtained by the same relationship (Equation (6)). The agreement between the Cp(p,T) data obtained by the acoustic method (this work) and densimetric one (reported by Safarov et al. [16]) is excellent, the RDs are in the range from −0.67 to 0.17% and AARD is 0.22% (see Figure 5).   [16,17,19] presented as relative deviations RDs (RD/% = 100·(ρ this work −ρ lit )/ρ this work ). The isentropic compressibility, κS, was determined from Equation (5) using the experimental speed of sound and determined density. The results are collected in Table 7. The overall expanded uncertainty of κS was estimated to be U(κS) = 1.5·10 −3 κS Pa −1 . The isentropic compressibility calculated from the speed of sound and density reported by Plantier et al. [15] is in an excellent agreement with those reported in this work. The RDs are in the range from −0.31% to 0.16% (see Figure 6), the AARD is 0.16%. The RDs between κS obtained from pρT data reported by Safarov et al. [16] and obtained in this work are in the range from −0.004% to 6.3% (see Figure 6), the AARD is 2.1%.  The isentropic compressibility, κ S , was determined from Equation (5) using the experimental speed of sound and determined density. The results are collected in Table 7. The overall expanded uncertainty of κ S was estimated to be U(κ S ) = 1.5·10 −3 κ S Pa −1 . The isentropic compressibility calculated from the speed of sound and density reported by Plantier et al. [15] is in an excellent agreement with those reported in this work. The RDs are in the range from −0.31% to 0.16% (see Figure 6), the AARD is 0.16%. The RDs between κ S obtained from pρT data reported by Safarov et al. [16] and obtained in this work are in the range from −0.004% to 6.3% (see Figure 6), the AARD is 2.1%.  Based on the temperature dependence of density, the isobaric thermal expansion was calculated using a definition (Equation (4)). The obtained results are collected in Table 8. The overall expanded uncertainty of αp is U(αp) = 1·10 −2 αp K −1 . The agreement with literature data is very good, the RDs are in the range from −1.9 to 0.17% [16] and from −2.2 to 0.19% [17] (see Figure 7). The AARD is 0.83% [16] and 1.0% [17].  [15,16] presented as relative deviations RDs (RD/% = 100·(κ S , this work − κ S , lit )/κ S , this work ); * calculated from the pρT data [16].
Based on the temperature dependence of density, the isobaric thermal expansion was calculated using a definition (Equation (4)). The obtained results are collected in Table 8. The overall expanded uncertainty of α p is U(α p ) = 1·10 −2 α p K −1 . The agreement with literature data is very good, the RDs are in the range from −1.9 to 0.17% [16] and from −2.2 to 0.19% [17] (see Figure 7). The AARD is 0.83% [16] and 1.0% [17].  For the comprehensive characterization of the tested liquid, the compressibility at a constant temperature, κT, is the next important material constant. In this work, κT was calculated from κS using Eq. (3), the results are listed in Table 9. The overall expanded uncertainty of κT was estimated to be U(κT) = 5·10 −3 κT Pa −1 . In this work, the κT was obtained by the acoustic method based on integration procedures. On the other hand, the κT obtained by the densimetric method is based on differentiation procedures [16,17]. The RDs between results obtained in this work using the acoustic method and literature data obtained using the densimetric method are in the range from −0.08 to 5.2% [16] and from −3.5 to −1.5% [17] (see Figure 8). The AARD is 1.6% [16] and 2.7% [17]. Table 9. The isothermal compressibility, κT, of 1-butanol at pressures up to 100 MPa and within the temperature range from (293 to 318) K. For the comprehensive characterization of the tested liquid, the compressibility at a constant temperature, κ T , is the next important material constant. In this work, κ T was calculated from κ S using Eq. (3), the results are listed in Table 9. The overall expanded uncertainty of κ T was estimated to be U(κ T ) = 5·10 −3 κ T Pa −1 . In this work, the κ T was obtained by the acoustic method based on integration procedures. On the other hand, the κ T obtained by the densimetric method is based on differentiation procedures [16,17]. The RDs between results obtained in this work using the acoustic method and literature data obtained using the densimetric method are in the range from −0.08 to 5.2% [16] and from −3.5 to −1.5% [17] (see Figure 8). The AARD is 1.6% [16] and 2.7% [17].  The molar isochoric heat capacity, CV, was calculated using the experimental speed of sound as well as the determined density, molar isobaric heat capacity and isobaric thermal expansion: The CV values obtained in this work are collected in Table 10. The overall expanded uncertainty of CV was estimated to be U(CV) = 2·10 −2 CV J·mol −1 ·K −1 . The CV values obtained in this work by the acoustic method and those obtained using the densimetric method by Safarov et al. [16] are in excellent agreement. The RDs are in the range from −0.19 to 1.1% [16] (see Figure 9) and AARD is 0.35% [16].  The molar isochoric heat capacity, C V , was calculated using the experimental speed of sound as well as the determined density, molar isobaric heat capacity and isobaric thermal expansion: The C V values obtained in this work are collected in Table 10. The overall expanded uncertainty of C V was estimated to be U(C V ) = 2·10 −2 C V J·mol −1 ·K −1 . The C V values obtained in this work by the acoustic method and those obtained using the densimetric method by Safarov et al. [16] are in excellent agreement. The RDs are in the range from −0.19 to 1.1% [16] (see Figure 9) and AARD is 0.35% [16].  The internal pressure was calculated using the experimental speed of sound and determined density, isobaric heat capacity, and isobaric thermal expansion: The results are collected in Table 11. The overall expanded uncertainty of pint was estimated to be U(pint) = 1·10 −2 pint Pa. The RDs for pint obtained in this work by the acoustic method and those obtained by the densimetric method are in the range from −6.3 to −0.36% [16] and from −0.21 to 3.0% [17] (see Figure 10). The AARD is 2.7% [16] and 1.7% [17].  The internal pressure was calculated using the experimental speed of sound and determined density, isobaric heat capacity, and isobaric thermal expansion: The results are collected in Table 11. The overall expanded uncertainty of p int was estimated to be U(p int ) = 1·10 −2 p int Pa. The RDs for p int obtained in this work by the acoustic method and those obtained by the densimetric method are in the range from −6.3 to −0.36% [16] and from −0.21 to 3.0% [17] (see Figure 10). The AARD is 2.7% [16] and 1.7% [17].  The relative deviations RDs ( Figure 10) suggest that the pressure dependence of the internal pressure of 1-butanol is different depending on the data source (see Figure 11). Figure 11. Comparison of the internal pressure of 1-butanol as a function of pressure obtained in this work with those obtained from the pρT literature data [16,17].
The relative deviations RDs (Figure 10) suggest that the pressure dependence of the internal pressure of 1-butanol is different depending on the data source (see Figure 11). The relative deviations RDs ( Figure 10) suggest that the pressure dependence of the internal pressure of 1-butanol is different depending on the data source (see Figure 11). Figure 11. Comparison of the internal pressure of 1-butanol as a function of pressure obtained in this work with those obtained from the pρT literature data [16,17].
The density, isentropic compressibility and isobaric thermal expansion of 1-butanol were compared with density, isentropic compressibility and isobaric thermal expansion of heptane [36,37], ethanol [36,37], dodecane [38], diesel oil (ekodiesel ultra) [12] and biodiesel [12]. Heptane and dodecane are components of the fuels [36][37][38]. The engine simulations were carried out first using heptane and then dodecane as a more suitable "low or no sulphur", "ideal" surrogate component for petrodiesel fuels [39,40]. Moreover, the thermophysical properties of dodecane are similar to the thermophysical properties of aviation kerosene [41]. For comparison, ethanol was also chosen as the most commonly used bioalcohol. Additionally, the properties of 1-butanol were Figure 11. Comparison of the internal pressure of 1-butanol as a function of pressure obtained in this work with those obtained from the pρT literature data [16,17].
The density, isentropic compressibility and isobaric thermal expansion of 1-butanol were compared with density, isentropic compressibility and isobaric thermal expansion of heptane [36,37], ethanol [36,37], dodecane [38], diesel oil (ekodiesel ultra) [12] and biodiesel [12]. Heptane and dodecane are components of the fuels [36][37][38]. The engine simulations were carried out first using heptane and then dodecane as a more suitable "low or no sulphur", "ideal" surrogate component for petrodiesel fuels [39,40]. Moreover, the thermophysical properties of dodecane are similar to the thermophysical properties of aviation kerosene [41]. For comparison, ethanol was also chosen as the most commonly used bioalcohol. Additionally, the properties of 1-butanol were compared with those of petrodiesel oil with sulfur content < 10 mg/kg which fulfilled norm EN 590 [12] (named ekodiesel ultra) and biodiesel composed of fatty acid methyl esters from rapeseed oil, which fulfilled norm EN 14214 [12]. Among studied fuel components, the density of 1-butanol at 288.15 K is the closest to norm EN 590 for diesel and the most similar to the density of diesel oil ekodiesel ultra (see Figure 12). Moreover, the differences between the density of 1-butanol and ekodiesel ultra decrease with increasing pressure from 2.8% at 0.1 MPa to 1.9% at 100 MPa and at 298.15 K (see Figure 13). compared with those of petrodiesel oil with sulfur content < 10 mg/kg which fulfilled norm EN 590 [12] (named ekodiesel ultra) and biodiesel composed of fatty acid methyl esters from rapeseed oil, which fulfilled norm EN 14214 [12]. Among studied fuel components, the density of 1-butanol at 288.15 K is the closest to norm EN 590 for diesel and the most similar to the density of diesel oil ekodiesel ultra (see Figure 12). Moreover, the differences between the density of 1-butanol and ekodiesel ultra decrease with increasing pressure from 2.8% at 0.1 MPa to 1.9% at 100 MPa and at 298.15 K (see Figure 13). Figure 12. Comparison of the density at 288.15 K of heptane [36,37], dodecane [38], ethanol [36,37], 1-butanol (this work), ekodiesel ultra [12], biodiesel [12] with norm EN 590 for diesel and EN 14214 for biodiesel. Figure 13. The pressure dependence of density of heptane and dodecane-fuel components, ethanol-the most common used bioalcohol, low sulfur diesel oil (ekodiesel ultra) and biodiesel (FAME) at 298.15 K.  [36,37], dodecane [38], ethanol [36,37], 1-butanol (this work), ekodiesel ultra [12], biodiesel [12] with norm EN 590 for diesel and EN 14214 for biodiesel.
Energies 2019, 12, x FOR PEER REVIEW 15 of 21 compared with those of petrodiesel oil with sulfur content < 10 mg/kg which fulfilled norm EN 590 [12] (named ekodiesel ultra) and biodiesel composed of fatty acid methyl esters from rapeseed oil, which fulfilled norm EN 14214 [12]. Among studied fuel components, the density of 1-butanol at 288.15 K is the closest to norm EN 590 for diesel and the most similar to the density of diesel oil ekodiesel ultra (see Figure 12). Moreover, the differences between the density of 1-butanol and ekodiesel ultra decrease with increasing pressure from 2.8% at 0.1 MPa to 1.9% at 100 MPa and at 298.15 K (see Figure 13). Figure 12. Comparison of the density at 288.15 K of heptane [36,37], dodecane [38], ethanol [36,37], 1-butanol (this work), ekodiesel ultra [12], biodiesel [12] with norm EN 590 for diesel and EN 14214 for biodiesel. Figure 13. The pressure dependence of density of heptane and dodecane-fuel components, ethanol-the most common used bioalcohol, low sulfur diesel oil (ekodiesel ultra) and biodiesel (FAME) at 298.15 K. The 1-butanol is less compressible than heptane by 43 ÷ 20% in the pressure range of 0.1 ÷ 100 MPa, and ethanol by 21 ÷ 12% in the pressure range of 0.1 ÷ 90 MPa at 298.15 K. The 1-butanol is more compressible than diesel by 18 ÷ 12% and biodiesel by 28 ÷ 17% in the pressure range of 0.1 ÷ 100 MPa at 298.15 K. On the other hand, the compressibility of 1-butanol is close to dodecane, and furthermore, the differences between compressibility of 1-butanol and dodecane decrease with increasing pressure from 1.5% at 0.1 MPa to 0.5% at 100 MPa and at 298.15 K (Figure 14). The 1-butanol is less compressible than heptane by 43 ÷ 20% in the pressure range of 0.1 ÷ 100 MPa, and ethanol by 21 ÷ 12% in the pressure range of 0.1 ÷ 90 MPa at 298.15 K. The 1-butanol is more compressible than diesel by 18 ÷ 12% and biodiesel by 28 ÷ 17% in the pressure range of 0.1 ÷ 100 MPa at 298.15 K. On the other hand, the compressibility of 1-butanol is close to dodecane, and furthermore, the differences between compressibility of 1-butanol and dodecane decrease with increasing pressure from 1.5% at 0.1 MPa to 0.5% at 100 MPa and at 298.15 K (Figure 14). Figure 14. The pressure dependence of isentropic compressibility of heptane and dodecane-fuel components, ethanol-the most common used bioalcohol, low sulfur diesel oil (ekodiesel ultra) and biodiesel (FAME) at 298.15 K.
As in the case of isentropic compressibility, the isobaric thermal expansion of 1-butanol is lower than those of heptane by 32 ÷ 15% in the pressure range of 0.1 ÷ 100 MPa, and ethanol 15 ÷ 12% in the pressure range of 0.1 ÷ 90 MPa at 298.15 K. The isobaric thermal expansion of 1-butanol is higher than those of diesel by 10 ÷ 7% and biodiesel by 12 ÷ 5% in the pressure range of 0.1 ÷ 100 MPa at 298.15 K. On the other hand, isobaric thermal expansion of 1-butanol is the most similar to dodecane and likewise, the pressure dependence of isobaric thermal expansion of 1-butanol is the most similar to the pressure dependence of isobaric thermal expansion of dodecane ( Figure 15). The differences between the expansivity of 1-butanol and dodecane slightly decrease with increasing pressure from 3.3% at 0.1 MPa to 2.9% at 100 MPa and at 298.15 K. Figure 14. The pressure dependence of isentropic compressibility of heptane and dodecane-fuel components, ethanol-the most common used bioalcohol, low sulfur diesel oil (ekodiesel ultra) and biodiesel (FAME) at 298.15 K.
As in the case of isentropic compressibility, the isobaric thermal expansion of 1-butanol is lower than those of heptane by 32 ÷ 15% in the pressure range of 0.1 ÷ 100 MPa, and ethanol 15 ÷ 12% in the pressure range of 0.1 ÷ 90 MPa at 298.15 K. The isobaric thermal expansion of 1-butanol is higher than those of diesel by 10 ÷ 7% and biodiesel by 12 ÷ 5% in the pressure range of 0.1 ÷ 100 MPa at 298.15 K. On the other hand, isobaric thermal expansion of 1-butanol is the most similar to dodecane and likewise, the pressure dependence of isobaric thermal expansion of 1-butanol is the most similar to the pressure dependence of isobaric thermal expansion of dodecane ( Figure 15). The differences between the expansivity of 1-butanol and dodecane slightly decrease with increasing pressure from 3.3% at 0.1 MPa to 2.9% at 100 MPa and at 298.15 K.
The internal pressure is related to the solubility parameter [42][43][44][45][46][47][48] and cohesive energy density [43,46,49]. According to the definition, the internal pressure reflects molecular interactions which determine the change of internal energy that accompanying a very small isothermal expansion of 1 mole of liquid. Therefore, the internal pressure should be affected mainly by dispersion, repulsion, and weak dipole-dipole interactions. Kartsev et al. [50][51][52][53] pointed out that the temperature dependence of internal pressure is sensitive to the structural organization and reflects the character of the interactions of not hydrogen-bonded, hydrogen-bonded with the spatial net of H-bonds and associated liquids. They showed that, at atmospheric pressure, the sign reversal of the temperature coefficient of the internal pressure from (∂p int /∂T) p > 0 to (∂p int /∂T) p < 0 is characteristic for primary linear alkanols. Our group found that the pressure coefficient of internal pressure (∂p int /∂p) T is also sensitive to the structural organization of the molecular liquids like alcohols [20,54,55] as well as ionic liquids [56] and reflects the character of the interactions. The temperature and pressure dependence of the internal pressure of 1-butanol found in this work confirms the results obtained previously for 1-alkanols [20,54,55]. In the temperature and pressure ranges under investigation, the maximum of the pressure dependence of the internal pressure of 1-butanol was observed for each isotherm (see Figure 16). With increasing temperature, the maximum moves toward higher pressures. Thus, the internal pressure first increases with increasing pressure and then it decreases. This was also observed for ethanol and for other 1-alkanols from 1-pentanol to 1-decanol [20,54,55]. The internal pressure of 1-butanol obtained by Safarov et al. [16] decreases with increasing pressure ((∂p int /∂p) T < 0) in the pressure range under investigation and at temperatures as in this work. Meanwhile, the internal pressure of 1-butanol obtained by Dávila et al. [17] increases with increasing pressure ((∂p int /∂p) T > 0) in the pressure range under investigation and at temperatures as in this work. Moreover, the results obtained in this work shows that with the increasing pressure, the temperature dependence of the internal pressure of 1-butanol changes from (∂p int /∂T) p < 0 to (∂p nt /∂T) p > 0. This reflects the crossing point of the isotherms of the internal pressure, which was observed for ethanol and for other 1-alkanols from 1-pentanol to 1-decanol [20,54,55]. Dávila et al. [17] also found the crossing point of internal pressure isotherms of 1-butanol. On the other hand, Safarov et al. [16] did not observe this effect; (∂p int /∂T) p > 0 in the whole pressure range. The inspection of literature data shows better internal coherence of p int (p,T) dependence obtained by the acoustic method than obtained by the densimetric method. In the case of the densimetric method, isobaric thermal expansion and isothermal compressibility are obtained by differentiation using their definitions acquired by Equations (4) and (6), respectively. Meanwhile, in the acoustic method, differentiation is needed only for the determination of isobaric thermal expansion (Equation (4)). The crossing point of the internal pressure isotherms was also observed for 2-methyl-2-butanol and 3-pentanol [54,55]. For 3-pentanol, the crossing point of each two neighbor isotherms shifts toward higher pressure with increasing temperature [54,55]. For 2-methyl-2-butanol, the crossing point of each two neighbor isotherms appears at temperatures higher than 303.15 K and it moves toward higher pressure with increasing temperature as in the case of 3-pentanol [55]. On the other hand, for 2-methyl-1-butanol, the crossing point is not observed, and the internal pressure increases with increasing temperature over the whole investigated temperature and pressure range. However, the temperature dependence of the internal pressure of 2-methyl-1-butanol under atmospheric pressure indicates that the crossing point could appear at higher temperatures [55]. The internal pressure is related to the solubility parameter [42][43][44][45][46][47][48] and cohesive energy density [43,46,49]. According to the definition, the internal pressure reflects molecular interactions which determine the change of internal energy that accompanying a very small isothermal expansion of 1 mole of liquid. Therefore, the internal pressure should be affected mainly by dispersion, repulsion, and weak dipole-dipole interactions. Kartsev et al. [50][51][52][53] pointed out that the temperature dependence of internal pressure is sensitive to the structural organization and reflects the character Figure 15. The pressure dependence of isobaric thermal expansion of heptane and dodecane-fuel components, ethanol-the most common used bioalcohol, low sulfur diesel oil (ekodiesel ultra) and biodiesel (FAME) at 298.15 K. the crossing point is not observed, and the internal pressure increases with increasing temperature over the whole investigated temperature and pressure range. However, the temperature dependence of the internal pressure of 2-methyl-1-butanol under atmospheric pressure indicates that the crossing point could appear at higher temperatures [55].

Summary
The speed of sound in 1-butanol was conducted in the temperature range from (293 to 318) K and at pressures up to 101 MPa. The density of the liquid under test was measured within the temperatures from (293 to 318) K under atmospheric pressure. From the experimental results, the pressure and temperature dependence of the density, isobaric heat capacity and related thermodynamic properties such as isentropic and isothermal compressibilities, the isobaric thermal expansion and internal pressure as a function of temperature and pressure were determined using the acoustic method. The obtained results show that the density of 1-butanol is close to norm EN 590 for diesel oil and, as a consequence, is close to the density of ekodiesel ultra. The isobaric expansivity and isentropic compressibility of 1-butanol are close to those of dodecane-a surrogate component for petrodiesel fuels and aviation kerosene. The temperature and pressure dependence of the internal pressure, obtained by the acoustic method, qualitatively confirms similarities and dissimilarities of 1-butanol, other 1-alkanols as well as 2-methyl-2-butanol and 3-pentanol. Discrepancies in the sign of (∂pint/∂T)p and (∂pint/∂p)T were found for 1-butanol obtained by the acoustic method and densimetric method. Thus, the determination of internal pressure as a function of temperature and pressure is still an open, complex issue.

Summary
The speed of sound in 1-butanol was conducted in the temperature range from (293 to 318) K and at pressures up to 101 MPa. The density of the liquid under test was measured within the temperatures from (293 to 318) K under atmospheric pressure. From the experimental results, the pressure and temperature dependence of the density, isobaric heat capacity and related thermodynamic properties such as isentropic and isothermal compressibilities, the isobaric thermal expansion and internal pressure as a function of temperature and pressure were determined using the acoustic method. The obtained results show that the density of 1-butanol is close to norm EN 590 for diesel oil and, as a consequence, is close to the density of ekodiesel ultra. The isobaric expansivity and isentropic compressibility of 1-butanol are close to those of dodecane-a surrogate component for petrodiesel fuels and aviation kerosene. The temperature and pressure dependence of the internal pressure, obtained by the acoustic method, qualitatively confirms similarities and dissimilarities of 1-butanol, other 1-alkanols as well as 2-methyl-2-butanol and 3-pentanol. Discrepancies in the sign of (∂p int /∂T) p and (∂p int /∂p) T were found for 1-butanol obtained by the acoustic method and densimetric method. Thus, the determination of internal pressure as a function of temperature and pressure is still an open, complex issue.