Article pubs.acs.org/jced
Heat Capacities of Four Promising Alternatives to Lithium Bromide Aqueous Solution in Absorption Refrigerators Neng Gao, Guangming Chen, Yunyun Jiang, Lingyun Fang, and Yijian He* Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou, China, 310027 ABSTRACT: Properly choosing additives to conventional lithium bromide aqueous solution to improve the performance is an important part in lithium bromide absorption refrigeration studies. Mixtures consisting of lithium bromide + triethylene glycol + water, lithium bromide + propylene glycol + water, lithium bromide + sodium formate + water, and lithium bromide + potassium formate + water were thought to be four promising alternatives to lithium bromide aqueous solutions. In the study, heat capacities of the four kinds of solutions were measured using a calvet type calorimeter at temperatures from 308.15 K to 348.15 K. The experimental data were regressed using a stepwise statistical method, and the corresponding equations for each kind of solution were given. The average absolute deviations between experimental and calculated values were no more than 0.12 % for all of the systems.
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INTRODUCTION An increasing shortage of energy has been inspiring people to search for different kinds of sustainable technologies. Absorption heat pumps and absorption refrigerators have drawn great attention since the day these systems were proposed, for their ability to apply “low grade” heat sources as driving energies. Based on the working characters of these absorption systems, working fluids with specific thermodynamic properties are demanded. Lithium bromide plus water solution is the most widely used working pair due to its good performance in absorption systems, but there should be some improvements on its relatively high corrosivity at high concentrations and its unsatisfactory crystallization line. Physical and thermodynamic properties of aqueous lithium bromide and its performance in absorption systems have been discussed in detail by different researchers theoretically and experimentally.1,2 Despite the research on the solution, attention has also been focused on its alternatives consisting of the solution and some additives which were added to improve the performance characteristics. Since 1989, researchers from Kansai University have done a series of property measurements on lithium bromide plus water plus either organic amine (ethylamine) or electrolytical salts (zinc chloride, calcium bromide, zinc bromide, lithium chloride, lithium iodide, lithium nitrate) systems.3,4 De Lucas and his colleagues started in 2003 their research on properties of lithium bromide water solutions plus organic salts as additives for the purpose of reducing the vapor pressures, and they suggested the solutions with potassium formate and sodium formate as the two most promising alternative absorbents for absorption refrigeration systems.5 Organic glycols can also be used in absorption systems, and mixtures containing both glycols and aqueous lithium bromide have been studied by Li et al. in 2009.6 © 2013 American Chemical Society
Heat capacity is one of the most important properties for evaluating a new absorbent for its directly thermodynamic connection with enthalpy and its irreplaceability in basic thermodynamic equations. High quality data of heat capacities for both binary solution of lithium bromide plus water and its mixtures with certain additives would benefit the researchers in system thermodynamic calculations and electrolyte solution model studies. Abundant work have been completed on the heat capacity of lithium bromide aqueous solutions.7−9 But limited experimental studies could be found on the heat capacities of newly suggested mixtures, which is unsuitable given their essentialness in engineering applications and solution theory studies. That is the very motivation of our work. Four kinds of mixtures were investigated in the study, that is, lithium bromide plus triethylene glycol (mass ratio LiBr/TEG = 0.5), lithium bromide plus propylene glycol (mass ratio LiBr/ PG = 0.5), lithium bromide plus sodium formate (mass ratio LiBr/CHOONa = 2), and lithium bromide plus potassium formate (mass ratio LiBr/CHOOK = 2). Considering the solubility of the mixed solutes in water and the working conditions of these solutions in absorption machines, the experimental temperatures were chosen to range from 308.15 K to 348.15 K, and the mass fractions of mixed solutes were from 0.3 to 0.7 for (LiBr + glycols), 0.2 to 0.45 for (LiBr + CHOONa), and 0.2 to 0.4 for (LiBr + CHOOK), respectively. Received: June 26, 2013 Accepted: September 18, 2013 Published: October 8, 2013 3155
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Article
APPARATUS AND MATERIALS Materials. All of the materials used in the study were from Aladdin Chemistry Co. Ltd. (China). The purity of each compounds used in this study is given in Table 1. Water used in the study as solvent was deionized and double-distilled.
was set to be 308.15 K to 348.15 K. At each temperature, the heat capacities were measured once. The mass fractions of the mixed solutes for each kind of solution ranged from 0.3 to 0.7 for (LiBr + glycols), 0.2 to 0.45 for (LiBr + CHOONa), and 0.2 to 0.4 for (LiBr + CHOOK), respectively.
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RESULTS AND DISCUSSION The obtained heat capacities for each solution at different temperatures and mass fractions were shown in Table 2 to 5.
Table 1. Source and Purity of the Experimental Compounds chemical name lithium bromide sodium formate potassium formate propylene glycol triethylene glycol
source Aladdin Chemistry Co. Ltd. (China)
mass fraction purity 99.9 % 99.99 % 99 % 99 % 99.5 %
Table 2. Heat Capacities Cp of LiBr + TEG + H2O Solutions (LiBr/TEG = 0.5, by mass) at Different Temperatures T and Different Mixed Solute Mass Fractions w at Pressure p = 0.1 MPaa Cp/kJ·kg−1·K−1
No further purification was done for each component before the solutions were made on a Metter Toledo AL104 electronic balance. The balance has a resolution of 0.1 mg. Each solution sample weighted about 20 g to 30 g. Apparatus and Procedure. The main part of the measuring system is a C80 microcalorimeter from SETARAM (France). The calorimeter works on the Tian-Calvet principle and has a temperature repeatability of 0.05 K, a calorimetric resolution of 0.1 μW, and a temperature rising speed range from 0.1 K·min−1 to 2 K·min−1. More detailed information about the calorimeter has been introduced by Ficke et al.10 in his work in 2008. The inner calorimeter consists of two identical wells surrounded by hundreds of thermopiles. Two identically manufactured vessels were put into the bottom of the wells with one of them filled with the sample and the other remained empty. The vessels used in this study were specialized for liquid heat capacity measurements. The top of the vessel was welded with a tube, and the sample was filled into bottom of the vessel with a syringe. The filling was performed until the tube and the vessel were both full of liquid. In this way, it was guaranteed that the volume of the vessel surrounded in the heat detecting area was unchanged from the beginning of heating to the end. Therefore, the potential adverse impacts on the accuracy of the experiments from vapor vaporization and bubble formation were avoided. The temperature rising speed was set as 0.1 K·min−1 for all samples. The heat capacity data could be obtained as shown in eq 1, Cp = (HFsample − HFblank )/(ρsample V (dT/dt ))
T/K
w = 0.3
w = 0.4
w = 0.5
w = 0.6
w = 0.7
308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15
3.832 3.846 3.858 3.868 3.878 3.886 3.893 3.893
3.631 3.646 3.660 3.672 3.684 3.694 3.701 3.705
3.318 3.335 3.350 3.365 3.379 3.392 3.401 3.406
2.924 2.943 2.960 2.976 2.991 3.006 3.018 3.027
2.510 2.525 2.540 2.556 2.571 2.584 2.596 2.603
a Standard uncertainties u are u(T) = 0.05 K, u(w) = 0.001, u(p) = 5 kPa, and the combined expanded uncertainty Uc is Uc(Cp) = 0.007 kJ· kg−1·K−1 (0.95 level of confidence).
Table 3. Heat Capacities of Cp LiBr + PG + H2O Solutions (LiBr/PG = 0.5, by mass) at Different Temperatures T and Different Mixed Solute Mass Fractions w at Pressure p = 0.1 MPaa Cp/kJ·kg−1·K−1 T/K
w = 0.3
w = 0.4
w = 0.5
w = 0.6
w = 0.7
308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15
3.588 3.595 3.603 3.609 3.617 3.623 3.627 3.622
3.356 3.361 3.369 3.379 3.387 3.392 3.398 3.397
3.087 3.100 3.112 3.123 3.133 3.141 3.146 3.146
2.816 2.832 2.844 2.856 2.868 2.878 2.885 2.888
2.550 2.566 2.578 2.591 2.604 2.616 2.625 2.640
a Standard uncertainties u are u(T) = 0.05 K, u(w) = 0.001, and u(p) = 5 kPa, and the combined expanded uncertainty Uc is Uc(Cp) = 0.007 kJ·kg−1·K−1 (0.95 level of confidence).
(1)
where the heat flow of the sample vessel HFsample (W), the heat flow of the blank vessel HFblank (W), and the actual temperature rising speed (dT/dt) (K·s−1) were acquired in the C80 calorimeter. The densities of the samples ρsample (kg·m−3) were obtained under different temperatures and mass fractions before the experiments started. The volume of the vessel within the heat detecting area V is 14.0·10−6 m−3. The densities of the (LiBr + CHOONa) and (LiBr + CHOOK) aqueous solutions were calculated from De Lucas’s equation,5 and the densities of the (LiBr + PG) and (LiB + TEG) aqueous solutions were calculated from Lee’s equation.6 The density equations were empirical functions of temperatures and mass fractions and were given upon the basement of their experimental results of the densities at different conditions. To cover the working conditions of the solutions in absorption refrigerators, the experiment temperature range
Based on the experimental results, empirically correlated equations for thermodynamic calculation in engineering applications were obtained for each kind of solution with a uniform expression as eq 2: N
Cp =
∑ aiτ n wm i
i=1
i
(2)
where τ is the dimensionless temperature τ = T/(100 K) and w is the mass fraction of the absorbent. ni and mi are the polynomial orders for τ and w, and ai represent the correlated parameters. A stepwise statistical method was used during the correlation for the purpose of reducing the essential terms of the equation without decrease in accuracy. The average 3156
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Table 4. Heat Capacities Cp of LiBr + CHOONa + H2O Solutions (LiBr/CHOONa = 2, by mass) at Different Temperatures T and Different Mixed Solute Mass Fractions w at Pressure p = 0.1 MPaa
absolute deviation (AAD) and maximum deviation (MAD) were used to evaluate the correlation of the equations. The ai parameters and corresponding AAD% and MAD% for each system are listed in Table 6. The maximum of AAD% and MAD% were 0.12 % and 0.30 %, respectively, which showed a good matching between the experimental and the calculated heat capacities. Figures 1 to 4 show the heat capacity variations for each kind of solution with respect to temperatures. For all of these four
Cp/kJ·kg−1·K−1 T/K
w = 0.2
w = 0.3
w = 0.4
w = 0.45
308.15 313.16 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15
3.399 3.404 3.409 3.413 3.416 3.418 3.419 3.420 3.420 3.418
3.099 3.105 3.110 3.114 3.117 3.120 3.122 3.123 3.123 3.125
2.747 2.749 2.752 2.753 2.754 2.754 2.754 2.754 2.753 2.752
2.631 2.632 2.633 2.634 2.634 2.634 2.634 2.633 2.633 2.635
a Standard uncertainties u are u(T) = 0.05 K, u(w) = 0.001, and u(p) = 5 kPa, and the combined expanded uncertainty Uc is Uc(Cp) = 0.010 kJ·kg−1·K−1 (0.95 level of confidence).
Table 5. Heat Capacities of Cp LiBr + CHOOK + H2O Solutions (LiBr/CHOOK = 2, by mass) at Different Temperatures T and Different Mixed Solute Mass Fractions w at Pressure p = 0.1 MPaa Cp/kJ·kg−1·K−1 T/K
w = 0.2
w = 0.3
w = 0.4
308.15 313.16 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15
3.334 3.337 3.337 3.337 3.336 3.336 3.338 3.340 3.341 3.342
3.027 3.032 3.035 3.037 3.037 3.036 3.033 3.029 3.025 3.021
2.625 2.631 2.637 2.641 2.645 2.647 2.648 2.649 2.649 2.651
Figure 1. Heat capacities of (LiBr + TEG) (LiBr:TEG = 0.5, mass) aqueous solutions at different temperatures: ■, w = 0.3; ●, 0.4; ▲, 0.5; ▼, 0.6; ◀, 0.7, experimental data; lines, calculated from eq 2.
systems, when the temperature rises, the heat capacities increase, at extremely slow speeds. The heat capacities changes were indistinctive within the experiment temperature ranges. Figure 5 shows that at a certain temperature (T = 328.15 K, for example), for all of these solutions, when the mass fractions of the mixed solutes get higher, the heat capacities get smaller. At the same mass fractions, heat capacities of (LiBr + CHOONa) solutions were higher than those of (LiBr + CHOOK) solutions, and also the heat capacities of (LiBr + TEG) solutions were higher than (LiBr + PG) solutions (Figure 6). But at w = 0.7, the heat capacity of LiBr/TEG solution and
a
Standard uncertainties u are u(T) = 0.05 K, u(w) = 0.001, and u(p) = 5 kPa, and the combined expanded uncertainty Uc is Uc(Cp) = 0.016 kJ·kg−1·K−1 (0.95 level of confidence).
Table 6. Parameters of eq 2 for Different Kinds of Solutions
a
ai (n, m)
LiBr + TEG
LiBr + PG
(0, 0) (0, 1) (0, 2) (0, 3) (1, 0) (1, 1) (1, 2) (1, 3) (2, 0) (2, 1) (2, 2) (2, 3) AADa MADa no. points
3.3674 3.0754 −13.593 8.1023
4.0121 −6.3027 −4.1062 2.3958
0.64077
3.3247
LiBr + CHOONa
3.4171
−28.962 32.015 −0.2853 3.2352
−20.848
12.804 −8.6011 0.088556 −0.76749
−0.48245 −0.45644
0.12 % 0.30 % 40
LiBr + CHOOK
3.6453
−1.4606 1.3072 0.06 % 0.26 % 40
0.10 % 0.24 % 40
0.05 % 0.13 % 30
AAD% = (ΣNi=1|(Cpcal − Cpexp)/Cpexp|·100)/N, and MAD% = Max(|Cpcal − Cpexp)/Cpexp|·100)N. 3157
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Figure 2. Heat capacities of (LiBr + PG) (LiBr:PG = 0.5, mass) aqueous solutions at different temperatures: ■, w = 0.3; ●, 0.4; ▲, 0.5; ▼, 0.6; ◀, 0.7, experimental data; lines, calculated from eq 2.
Figure 5. Heat capacities of four different kinds of systems at T = 328.15 K: ■, (LiBr + TEG); ●, (LiBr + PG); ▲, (LiBr + CHOONa); ▼, (LiBr + CHOOK), experimental data; lines, calculated from eq 2.
Figure 3. Heat capacities of (LiBr + CHOONa) (LiBr:CHOONa = 2, mass) aqueous solutions at different temperatures: ▲, w = 0.2; ■, 0.3; ●, 0.4; ▼, 0.45, experimental data; lines, calculated from eq 2.
Figure 6. Relative differences (Cpexp − Cpcal)/Cpcal of the experimental heat capacity Cpexp from the value obtained from eq 2 Cpcal. ■, (LiBr + TEG), w = 0.3; ●, (LiBr + TEG), w = 0.4; ▲, (LiBr + TEG), w = 0.5; ▼, (LiBr + TEG), w = 0.6; ★, (LiBr + TEG), w = 0.7; □, (LiBr + PG), w = 0.3; ○, (LiBr + PG), w = 0.4; △, (LiBr + PG), w = 0.5; ▽, (LiBr + PG), w = 0.6; ☆, (LiBr + PG), w = 0.7, ⬓, (LiBr + CHOOK), w = 0.2; ◨, (LiBr + CHOOK), w = 0.3; ⬒, (LiBr + CHOOK), w = 0.4; ◓, (LiBr + CHOONa), w = 0.2; ◑, (LiBr + CHOONa), w = 0.3; ◒, (LiBr + CHOONa), w = 0.4; ◐, (LiBr + CHOONa), w = 0.45.
LiBr/PG solution are almost the same, which means the heat capacity of (LiBr + TEG) solution decreases faster than (LiBr + PG) solution. Also from Figure 5, it could be conjectured that, at the same mass fractions, the heat capacities of (LiBr + glycol) solutions are higher than (LiBr + formate) solutions. Uncertainty. According to the law of propagation of uncertainty, the expanded combined uncertainty of the heat capacities Uc could be obtained by: Uc = k
∑ (∂Cp/∂Xi)2 ·(u X )2 i
i
Figure 4. Heat capacities of (LiBr + CHOOK) (LiBr:CHOOK = 2, mass) aqueous solutions at different temperatures: ▲, w = 0.2; ■, 0.3; ●, 0.4, experimental data; lines, calculated from eq 2.
(3)
where Xi include all of the variables in the derivation of heat capacity, that is, the heat flows HFsample and HFblank, the density of the solution ρsample, the vessel volume V, and the temperature rise speed ∂T/∂t. All of the uncertainties of the variables for 3158
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Table 7. Uncertainties for Different Kinds of Solutions LiBr + TEG
LiBr + PG
LiBr + CHOONa
LiBr + CHOOK
uHFsample/w
8.1·10−5
8.2·10−5
8.8·10−5
8.6·10−5
uHFblank/w
1.2·10−7
1.2·10−7
1.2·10−7
1.2·10−7
−9
−9
−9
1.3·10−9 1.8·10−7 3.1 0.016
3
uV/m u∂T/∂t/K·s−1 uρ/kg·m−3 Uc/kJ·kg−1·K−1
1.3·10 2.0·10−7 0.21 0.007
1.3·10 3.4·10−7 0.34 0.007
sodium formate) system and (water plus lithium bromide plus potassium formate) system. J. Chem. Eng. Data 2003, 48, 756−756. (6) Tsai, C. Y.; Soriano, A. N.; Li, M. H. Vapour pressures, densities, and viscosities of the aqueous solutions containing (triethylene glycol or propylene glycol) and (LiCl or LiBr). J. Chem. Thermodyn. 2009, 41, 623−631. (7) Iyoki, S.; Uemura, T. Heat capacity of the water lithium bromide system and the water lithium bromide zinc bromide lithium chloride system at high temperatures. Int. J. Refrig. 1989, 12, 323−326. (8) Jeter, S. M.; Moran, J. P.; Teja, A. S. Properties of lithium bromide−water systems at high temperatures and concentrations Part III: specific heat. ASHRAE Trans. 1992, 98, 137−149. (9) Yuan, Z.; Herold, K. E. Specific heat measurements on aqueous lithium bromide. HVAC&R Res. 2005, 11, 361−375. (10) Ficke, L. E.; Rodriguez, H.; Brennecke, J. F. Heat capacities and excess enthalpies of 1-ethyl −3-methylimidazolium-based ionic liquids and water. J. Chem. Eng. Data 2008, 53, 2112−2119.
different kinds of solutions were listed in Table 7. k is the coverage factor and k ≈ 2 in this study. From eq 3, the corresponding combined uncertainties Uc were calculated and also listed in Table 7. It could be found that the uncertainties of HFsample and ρsample have relatively larger impacts on the final Uc than the others in this method.
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CONCLUSIONS Four kinds of promising alternatives° to the commonly used lithium bromide aqueous solution in absorption refrigerators were investigated on their heat capacities. The alternatives consist of lithium bromide aqueous solution and properly chosen additives, namely: LiBr + TEG + H2O (LiBr/TEG = 0.5, mass), LiBr + PG + H2O (LiBr/PG = 0.5, mass), LiBr + CHOONa + H2O (LiBr/CHOONa = 2, mass), and LiBr + CHOOK + H2O (LiBr/CHOOK = 2, mass). The heat capacity values of these solutions were obtained at temperatures from 308.15 K to 353.15 K and absorbent mass fractions from 0.2 to 0.7. Based on the experimental results, an empirical correlation was proposed. Using a statistical method, the essential terms of the empirical equation were chosen, and corresponding parameters were obtained for different systems. The average absolute deviations and maximum absolute deviations between experimental results and calculated values were no more than 0.12 % and 0.30 %, respectively, which confirmed the proposed equation to be accurate enough for engineering calculations.
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1.3·10 2.8·10−7 1.7 0.010
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Funding
This work is financially supported by the National Basic Research Program of China, project no. 2010CB227304, and the program of the National Natural Science Foundation of China, under contract no. 51206140. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Mc Neely, L. A. Thermodynamic properties of aqueous solutions of lithium bromide. ASHRAE Trans. 1979, 85, 413−434. (2) Patek, J.; Klomfar, J. A computationally effective formulation of the thermodynamic properties of LiBr-H2O solutions from 273 to 500 K over full composition range. Int. J. Refrig. 2006, 29, 566−578. (3) Iyoki, S.; Uemura, T. Vapor pressure of the water−lithium bromide system and the water−lithium bromide−zinc bromide− lithium chloride system at high temperatures. Int. J. Refrig. 1989, 12, 78−282. (4) Iyoki, S.; Gouda, H.; Uemura, T. Heat capacities of ethylamine plus water plus lithium bromide from 313.15 K to 373.15 K. J. Chem. Eng. Data 1998, 43, 893−894. (5) De Lucas, A.; Donate, M.; Rodriguez, J. F. Vapor pressures, densities, and viscosities of the (water plus lithium bromide plus 3159
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