2254
Langmuir 2003, 19, 2254-2259
Thermodynamic Property Fields of an Adsorbate-Adsorbent System Hui T. Chua,*,† Kim C. Ng,‡ Anutosh Chakraborty,‡ and Nay M. Oo‡ Bachelor of Technology Program, Faculty of Engineering, National University of Singapore, Singapore 117576, Singapore, and Department of Mechanical Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore Received October 18, 2002. In Final Form: December 20, 2002 We have developed the complete thermodynamic property fields for a single-component adsorbent + adsorbate system. These equations enable us to compute the actual specific heat capacity, the partial enthalpy, and the entropy, which are essential for the analyses of single-component adsorption processes. Conventionally, the specific heat capacity of the adsorbate is assumed to correspond to its liquid phase specific heat capacity and more recently to that of its gas phase. We have shown that the actual specific heat capacity of the adsorbate could differ significantly from what has been conventionally assumed. A simple but improved expression for the adsorbate specific heat capacity is also proposed.
Introduction The physical adsorption process which occurs mainly within the pores of adsorbent and the external adsorbent surface requires knowledge of the adsorption characteristics over wide ranges of pressures and temperatures. Adsorption on a solid adsorbent is the fundamental process in the fields of separation processes,1 purification of gases,2 adsorption chiller3 and cryocooler4 design, and, more recently, hydrogen storage.5 The knowledge of thermodynamic property fields of adsorbent plus adsorbate systems is important, because it enables the adsorption process to be analyzed. Our present formulation of enthalpy, internal energy, and entropy as a function of pressure, temperature, and mass of adsorbate is an extension of our previous work6 which is based on the framework of Feuerecker et al.,7 originally developed for absorption systems. Lopatkin8 developed general equations for three differential and three integral heat capacities of an adsorbed substance on the surface of a solid adsorbent at constant pressure and constant excess adsorption value using adsorption thermodynamics. He explained that the differential and integral heat capacities * To whom correspondence should be addressed. E-mail: engcht@ nus.edu.sg. † Bachelor of Technology Program, Faculty of Engineering, National University of Singapore. ‡ Department of Mechanical Engineering, National University of Singapore. (1) Antos, D.; Morgenstern, A. S. Application of gradients in the simulated moving bed process. Chem. Eng. Sci. 2001, 56, 6667-6682. (2) Fedorov, A. N. Investigation and improvement of cryogenic adsorption purification of argon from oxygen. Gas Separation and Purification, Vol. 9, No. 2; Elsevier Science Ltd.: Oxford, U.K., 1995; pp 137-145. (3) Sakoda, A.; Suzuki, M. Fundamental study on solar powered adsorption cooling system. J. Chem. Eng. Jpn. 1984, 17 (1), 52-57. (4) Prakash, M. J.; Prasad, M.; Rastogi, S. C.; Akkimaradi, B. S.; Gupta, P. P.; Narayanamurty, H.; Srinivasan, K. Development of a laboratory model of activated charcoal-nitrogen adsorption cryocooler. Cryogenics, Vol. 40; Elsevier Science, 2000; pp 481-488. (5) Liu, C.; Yang, Q. H.; Tong, Y.; Cong, H. T.; Cheng, H. M. Volumetric hydrogen storage in single-walled carbon nanotubes. Appl. Phys. Lett. 2002, 80 (13), 2389-2391. (6) Chua, H. T.; Ng, K. C.; Malek, A.; Oo, N. M. General thermodynamic framework for understanding temperature-entropy diagram of batchwise operating thermodynamic cooling cycles. J. Appl. Phys. 2001, 89 (9), 5151-5158. (7) Feuerecker, G.; Scharfe, J.; Greiter, I.; Frank, C.; Alefed, G. Measurement of thermophysical properties of aqueous LiBr-solutions at high temperature and concentrations. Proc. Int. absorption heat pump conf. AES, New Orleans, LA, 1994; American Society of Mechanical Engineers: New York, 1994; pp 493-499. (8) Lopatkin, A. A. The Heat Capacity of Adsorbed Substances. Russ. J. Phys. Chem. 2001, 75 (6), 946-950.
are equal for ideal gases, as well as that the additional terms, arising from the temperature increment dT of the system, are added to the heat capacity of the gas when liquid-vapor systems are studied, but he did not elaborate on those additional terms. Myers9 developed the thermodynamic functions such as Gibbs free energy, enthalpy, and entropy on the basis of isothermal immersion of adsorbent in the gas phase for providing a complete description of the adsorbate plus adsorbent system. He reasoned that the heat capacity of the entire system (adsorbent + adsorbate) in the condensed phase and the gas phase could be estimated from the heat capacity of the pure solid adsorbent and the ideal gas heat capacities of the adsobate. He concluded that the heat capacity of the adsorbate is equal to its heat capacity in the perfect gas state. We will show in this article that the adsorbate specific heat capacity can differ significantly from his results in many practical situations. In this work, a combination of an adsorbent and a singlecomponent adsorbed adsorbate is taken as an adsorbent + adsorbate (or adsorbate + adsorbent) system, and thermodynamic equilibrium prevails between this system and the single-component unadsorbed gas phase. In this study we develop the complete formulation of some thermodynamic properties such as internal energy, partial enthalpy, partial entropy, and specific heat capacity. We shall make use of experimental isotherm data available from the literature10-15 that are of practical interest to highlight the significant difference between the conventional uncorrected form of the specific heat capacity and the improved simplified expression presented herein. (9) Myers, A. L. Thermodynamics of Adsorption in Porous Materials. AIChE J. 2002, 48, No. 1. (10) Prasad, M.; Akkimardi, B. S.; Rastogi, S. C.; Rao, R. R.; Srinivasan, K. Adsorption Characteristic of the Charcoal-Nitrogen system at 79-320 K and pressures to 5 MPa. Carbon 1996, 34 (11), 1401-1406. (11) Chan, C. K.; Tward, E.; Boudaie, K. I. Adsorption isotherms and heats of adsorption of hydrogen, neon, and nitrogen on activated charcoal. Cryogenics 1984, 451-459. (12) Benard, P.; Chahine, R. Determination of the Adsorption Isotherms of Hydrogen on Activated Carbons above the Critical Temperature of the Adsorbate over wide temperature and pressure ranges. Langmuir 2001, 17, 1950-1955. (13) Chua, H. T.; Ng, K. C. Chakraborty, A.; Oo, N. M.; Othman, M. A. Adsorption Characteristic of Silica Gel + Water Systems. J. Chem. Eng. Data 2002, 47, 1177-1181. (14) Prakash, M. J.; Mattern, A.; Prasad, M.; Subramanya, S. R.; Srinivasan, K. Adsorption parameters of activated charcoal from adsorption studies. Carbon 2000, 38, 1163-1168. (15) Akkimaradi, B. S.; Prasad, M.; Dutta, P.; Srinivasan, K. Adsorption of 1,1,1,2-Tetrafluoroethane on Activated Charcoal. J. Chem. Eng. Data 2001, 46 (2), 417-422.
10.1021/la0267140 CCC: $25.00 © 2003 American Chemical Society Published on Web 02/14/2003
Adsorbate-Adsorbent System
Langmuir, Vol. 19, No. 6, 2003 2255
Thermodynamic Property Fields of Adsorbent + Adsorbate System Mass Balance. The mass balance of the adsorbent + adsorbate system is represented by
m/amabe ) mt - VgasFgas
(1)
where mabe is the mass of adsorbent, mt is the total amount of gas in the system, Vgas is the gas phase volume, and Fgas is the gas phase density. m/a is the adsorbed quantity of adsorbate under equilibrium conditions. Enthalpy Energy and Entropy Balances. The full expressions of the extensive thermodynamic quantities (enthalpy, internal energy, and entropy) of a single-component adsorbate + adsorbent system at a constant mass of adsorbent, Mabe, are shown in the following equations (2-4), respectively.
∂H dm dT + ∫ ∫∂H ∂T ∂m
H(P,T,ma,Mabe) )
a
dP ) ∫∂H ∂P
+
( )
a
∫c T
Mabe
T0 p,abe
dT +
∫
∂H ∂ma
ma
0
dma +
P1(T,ma),T,Mabe
∫
maMsys
Fsys
0
(1 - TR)
( ) ∂P1 ∂ma
dma +
T,Mabe
∫
PMsys
P1
Fsys
(1 - TR) dP (2)
where Msys is the mass of the adsorbate + adsorbent system, Fsys is the adsorbate + adsorbent system density, and cp,abe is the specific heat capacity of the adsorbent.
U(P,T,ma,Mabe) )
∫dH - ∫
∂(PV) dT ∂T
∫
maMsys
0
Fsys
(TR - P1β)
∫ ∂m
∂(PV)
( ) ∂P1 ∂ma
∫
dma -
a
dma -
T,Mabe
∫
ma
0
∫c
∂(PV) dP ) Mabe ∂P
P1
[
T T0 p,abe
]
( )
Msys ∂Fsys 1 Fsys F 2 ∂ma sys
dT +
∫
dma -
P1,T,Mabe
( )
ma
0
∂H ∂ma
∫
dma -
P1(T,ma),T,Mabe
PMsys
P1
Fsys
(TR - Pβ) dP (3)
and
∂S ∂S dT + ∫ ∫∂T ∂m
S(P,T,ma,Mabe) )
dma +
a
∫
Mabe
Tcp,abe
T0
T
∂S dP ) ∫∂P
dT +
∫
( )
ma
0
∂S ∂ma
dma -
P1(T,ma),T,Mabe
∫
maMsys
Fsys
0
R
( ) ∂P1 ∂ma
dma -
T,Mabe
∫
PMsys
P1
Fsys
R dP (4)
where (∂H/∂ma)P1(T,ma),T,Mabe, (∂S/∂ma)P1(T,ma),T,Mabe, the isothermal compressibility factor of the system, β, and the thermal expansion factor of the system, R, are respectively
( ) ( ) ∂H ∂ma
P1(T,ma),T,Mabe
∂S ∂ma
[
( ) ( ) ∂Vsys ∂ma
) hg{P1(T,ma),T} - T νg{P1(T,ma),T} -
[
) sg{P1(T,ma),T} - νg{P1(T,ma),T} -
P1(T,ma),T,Mabe
β)
( )
1 ∂Fsys Fsys ∂P
∂Vsys ∂ma
]( ](
P1(T,ma),T,Mabe
P1(T,ma),T,Mabe
)
∂P1(T,ma) ∂T
)
∂P1(T,ma) ∂T
(5)
ma,Mabe
(6) ma,Mabe
(7)
T,ma,Mabe
and
R)-
( )
1 ∂Fsys Fsys ∂T
(8)
P,ma,Mabe
In eqs 2-4, (∂P1/∂ma)T relates to the isothermal characteristics of the single-component adsorbate + adsorbent system. Integration is performed first from an initial reference temperature, T0, to temperature T, at zero adsorbate, then from zero adsorbate to adsorbate mass ma, at constant T, and finally from saturated pressure P1(T,ma) to nonequilibrium pressure P at constant T and ma. Therefore, these equations are able to define the respective instantaneous state points of an adsorbent-adsorbate system during its adsorption and desorption processes insofar as local thermodynamic equilibrium could be assumed. In eqs 5 and 6, (∂P1/∂T)ma relates to the Clapeyron relation. These partial quantities depend on pressure and temperature. Equations 5 and 6 could be further expressed respectively as
( )
) hg{P1(T,ma),T} - ∆Hads
(9)
( )
) sg{P1(T,ma),T} -
∆Hads T
(10)
∂H ∂ma
P1(T,ma),T,Mabe
and
∂S ∂ma
P1(T,ma),T,Mabe
2256
Langmuir, Vol. 19, No. 6, 2003
Chua et al.
The total differential of the extensive enthalpy, internal energy, and entropy of the single-component adsorbate + adsorbent system can therefore be respectively given by
dH(P,T,ma,Mabe) ) Mabecp,abe dT +
[{ ∫
ma
[∫ (
( ))
∂P1 ∂ Msys (1 - TR) ∂T Fsys ∂ma
ma
0
∆Hads T
cp,g(P1,T) +
0
(
) (
)
] [∫ ( [∫ (
( )
P1∂T
P1∂m
P1(T,ma),T,Mabe
a
dU(P,T,ma,Mabe) ) Mabecp,abe dT +
[{ ∫
ma
cp,g(P1,T) +
0
[
∫
(
( )) ) ( ) )]
∂P1 ∂ Msys (TR - P1β) ∂T Fsys ∂ma
ma
0
[
∫ ∂T∂ P
P1
[(
(
(
Msys (TR - Pβ) Fsys
P1Msys ∂Fsys P1 Fsys F 2 ∂ma sys
) (
)
T P,ma,Mabe
dP -
P,ma,Mabe
dma -
P1,T
(
[
P
P1
a
(
Msys (1 - TR) Fsys
(
P1
P,ma
∂P1 ∂H dT + ∂T ∂m P1 a
Msys (TR - Pβ) Fsys
)
]
dma dT -
P1,T P,m ,M a abe
] ( ) ) ] (
)
∂P1 dT + P1 ∂T
dma dT -
( ) )
P1Msys ∂Fsys ∂ P1 ∂T Fsys Fsys2 ∂ma
) ]
Msys (1 - TR) dP (11) Fsys
} ]
)
∂∆Hads ∂T
ma
0
Msys (TR - Pβ) Fsys
∫ ∂m∂
P,T,Mabe
-
] [ ( ∫
dma dT -
]
(
dma dT +
dP dma +
( ) (
νg ∂νg ∆Hads ∂Vsys ∂Vsys ∂T νg νg ∂ma ∂ma
∆Hads T
P,ma,Mabe
)
} ]
P,ma
dP -
Msys (1 - TR) Fsys
∂
P
dma +
P1
)
)
∂∆Hads ∂T
-
Msys (1 - TR) Fsys
∂
P
dma dT +
T P,ma,Mabe
∂H ∂ma
( ) (
∂νg ∆Hads νg ∂Vsys ∂Vsys ∂T νg νg ∂ma ∂ma
dma -
P1(T,ma),T,Mabe
dP dma -
P,T,Mabe
)
Msys (TR - Pβ) dP (12) Fsys
and
[
]
Mabecp,abe dT + T
dS(P,T,ma,Mabe) )
[{ ∫
ma
0
cp,g(P1,T) +
∆Hads T
[∫ { ( ) } ∂ Msys ∂P1 R ∂T Fsys ∂ma
(
) (
)
P1
} ]
)
∂∆Hads ∂T
-
P,ma
dma
dT T
( ) ] ] [∫ ( ) ( ) [∫ ( ) ] ( )
ma
0
( ) (
νg ∂νg ∆Hads ∂Vsys ∂Vsys ∂T νg νg ∂ma ∂ma P
dma dT -
T P,ma,Mabe
∂S ∂ma
∂
P1∂T
Msys R Fsys
P,ma,Mabe
P
dma -
∂
P1∂m
P1(T,ma),T,Mabe
Msys R Fsys
dP -
a
Msys R Fsys
∂P1 dT + p1 ∂T
dP dma -
P,T,Mabe
Msys R dP (13) Fsys
From eqs 11-13, the partial enthalpy, internal energy, and entropy of adsorbate in the single-component adsorbate + adsorbent system can therefore be fully expressed respectively as
{
}
∂H(P,T,ma,Mabe) ∂ma
) P,T,Mabe
{
}
∂H(P1,T,ma,Mabe) ∂ma
+
P1,T,Mabe
∫
P
[
P1
{
}
∂U(P,T,ma,Mabe) ∂ma
P,T,Mabe
)
{
{
}
∂H(P,T,ma,Mabe) ∂ma
}
∂H(P1,T,ma,Mabe) ∂ma
∫
P
P1
{
[
≈
P,T,Mabe
{
- P1
P1,T,Mabe
{
[
sys
}
P,T,Mabe
≈
∂Fsys ∂ma
P,T,Mabe
}
sys
( ) } P,T,Mabe
}]
dP (14)
(15)
]
P1,T,Mabe
{
Msys
-
}
∂H(P1,T,ma,Mabe) ∂ma
∂2Fsys ∂ma ∂T
P1,T,Mabe
( )
Msys ∂Fsys 1 Fsys F 2 ∂ma
{
(1 - 2TR) - T
∂H(P1,T,ma,Mabe) ∂ma
2Msys ∂Fsys (TR - Pβ) 1Fsys Fsys ∂ma
∂U(P,T,ma,Mabe) ∂ma
{( )
Msys 1 (1 - TR) Fsys F 2
Fsys2
∂2Fsys ∂2Fsys +P T ∂ma ∂T ∂ma ∂P
P1,T,Mabe
}]
dP (16)
(17)
Adsorbate-Adsorbent System
Langmuir, Vol. 19, No. 6, 2003 2257
and
{
}
∂S(P,T,ma,Mabe) ∂ma
) P,T,Mabe
{
}
∂S(P1,T,ma,Mabe) ∂ma
{
}
∂S(P,T,ma,Mabe) ∂ma
+
P1,T,Mabe
≈ P,T,Mabe
{
∫
P
[ { ( )
P1
R 2 ∂Fsys Fsys Fsys ∂ma
P,T,Mabe
}
∂S(P1,T,ma,Mabe) ∂ma
}
-1 +
]
Msys ∂2Fsys dP F 2 ∂ma ∂T sys
(18)
(19)
P1,T,Mabe
Hence, for practical application, the partial properties of the adsorbate in the single-component adsorbate + adsorbent system at the nonequilibrium state may be approximated by those at the saturated (equilibrium) state with the same temperature and amount of adsorbate as shown in eqs 15, 17, and 19.6 The term {(P1/Fsys) - (P1Msys/Fsys2)(∂Fsys/∂ma)P1,T} in the formulations above could be significant at higher uptake. In general, the same term could also be significant when there is significant system volumetric change during adsorption/ desorption. For a single-component adsorbate + adsorbent system, with the assumptions of a temperature independent isosteric heat of adsorption, a constant system volume, a constant adsorbent specific heat capacity, and a small value of the gaseous phase (1/νg)(∂νg/∂T), it can be shown that the differential extensive enthalpy, internal energy, and entropy of the system reduce to the expressions of Chua et al.,6 viz.
[
dH(P,T,ma,Mabe) ) Mabecp,abe dT + ma cp,g(P1,T) +
[
]
∆Hads ∆Hads ∂νg Mabe dT + [hg(P1,T) - ∆Hads] dma + dP T νg ∂T Fabe
dU(P,T,ma,Mabe) ) Mabecp,abe dT + ma cp,g(P1,T) +
]
∆Hads ∆Hads ∂νg dT + [hg(P1,T) - ∆Hads] dma T νg ∂T
(20) (21)
and
dS(P,T,ma,Mabe) ) Mabecp,abe
[
] [
]
∆Hads ∆Hads ∂νg dT ∆Hads dT + ma cp,g(P1,T) + + sg(P1,T) dma T T νg ∂T T T
(22)
The first term on the right-hand side of eqs 20-22 refers to the thermodynamic property of the adsorbent, and the second and third terms refer to that of the adsorbate in the system. Equation 21 is important for the analysis of the energy transfer associated with a typical adsorption/desorption process where the volume of the adsorbent-adsorbate system does not change significantly during the process. It is therefore interesting to note that the difference between the conventionally used expression for the differential internal energy and eq 20 is ma[∆Hads/T - (∆Hads/νg)(∂νg/∂T)] dT + [hg{P1(T,ma)} - hg(P,T)] dma. Similarly, the difference between the conventionally used expression for the differential entropy and eq 22 is ma[∆Hads/T - (∆Hads/νg)(∂νg/∂T)](dT/T) + [sg{P1(T,ma)} - sg(P,T)] dma. When, however, the volume of the adsorbent-adsorbate system does change significantly, the additional effect of {P1/Fsys - (P1Msys)/Fsys2(∂Fsys/∂ma)P1,T} in eq 12 may have to be considered. Specific Heat Capacity. The specific heat capacity of the adsorbate has for a long time been assumed to be equal to the liquid-phase specific heat capacity.16-18 Recently some researchers view the specific heat capacity of the adsorbate to be equal to the gas-phase specific heat capacity,19-21 which is defined as
cgs ) cp,abe +
ma c (P ,T) Mabe p,g 1
(23)
We propose that the specific heat capacity of the adsorbent + adsobate system can be adequately represented by
cas ) cp,abe +
[
]
ma ∆Hads ∆Hads ∂νg cp,g(P1,T) + Mabe T νg ∂T
(24)
The correction due to (ma/Mabe)[∆Hads/T - (∆Hads/νg)(∂νg/∂T)] turns out to be significant, because of the large isosteric heat of adsorption and the nonideality of the gas phase. This term represents the effect of the adsorbent in the adsorbed phase. The newly interpreted specific heat capacity can be significantly different from the gas phase specific heat capacity, and eq 24 reduces to eq 23 in the limit of low pressure and high temperature. The difference between the newly interpreted specific heat capacity and the specific heat capacity which assumes a gaseous phase adsorbate of a single-component adsorbent + adsorbate system is written as
∆cp ) |cas - cgs|
(25)
2258
Langmuir, Vol. 19, No. 6, 2003
Figure 1. Different specific heat capacities of a type-A silica gel + water system at 304 K: (4) the newly interpreted specific heat capacity; (0) the specific heat capacity of the adsorbent + adsorbate system by assuming a gas phase adsorbate; (O) the specific heat capacity of the system by assuming a liquid phase adsorbate.
Chua et al.
Figure 2. Different specific heat capacities of a type-A silica gel + water system at 338 K: (4) the newly interpreted specific heat capacity; (0) the specific heat capacity of the adsorbent + adsorbate system by assuming a gas phase adsorbate; (O) the specific heat capacity of the system by assuming a liquid phase adsorbate.
Results and Discussion From the literature,16-21 the specific heat capacity of the adsorbent-adsorbate system is comprised of two parts; one is the specific heat of the solid adsorbent, and the other is the contribution of the adsorbate at different isothermal conditions. Some researchers assume that the adsorbate is in a liquid state,16-18 and more recently some regard the adsorbate as a vapor phase19-21 in their design of adsorption processes. We calculated three different specific heat capacities, namely the newly interpreted specific heat capacity, the specific heat capacity assuming gaseous adsorbate, and the specific heat capacity assuming a liquid adsorbate phase in a single-component adsorbent + adsorbate system. Representative experimental isotherm data obtained from the literature10-15 are used in the demonstration of the correction to the system specific heat capacity offered by our proposed expression. These pertain to silica gel + water vapor, activated carbon + nitrogen, activated carbon + hydrogen, activated carbon + neon, and activated carbon + HFC134a systems. For silica gel + water and activated charcoal + HFC134a systems, the specific heat capacity assuming a liquid adsorbed phase is included in the comparison. But for activated carbon + nitrogen and activated carbon + hydrogen systems, the specific heat capacity assuming a liquid phase is excluded, as the adsorbed states are above the critical ranges. Figures 1 and 2 show the specific heat capacities of a silica gel + water system. Three different types of heat capacities are plotted. ∆cp is significant by as much as 30%; this difference is especially high along low-temperature isotherms. At 304 K cas is higher than cgs and the specific heat capacity assuming a liquid adsorbate phase, cls, but cas is lower than cls at 338 K. This is due to the characteristics of the nonideal gas phase. ∆cp decreases with increasing temperature as the gas phase (16) Ruthven, D. M. Principles of adsorption and adsorption processes; John Wiley & Sons: New York, 1984. (17) Suzuki, M. Adsorption engineering; Elsevier: Amsterdam, The Netherlands, 1990. (18) Tien, C. Adsorption calculation and modeling; ButterworthHeinemann series in chemical engineering; Boston, 1994. (19) Saha, B. B.; Boelman, E. C.; Kashiwagi, T. Computer simulation of a silica gel water adsorption refrigeration cycle-the influence of operating conditions on cooling output and COP. ASHRAE Trans. Res. 1995, 101 (2), 348-357. (20) Sami, S. M.; Tribes, C. An improved model for predicting the dynamic behaviour of adsorption systems. Appl. Therm. Eng. 1996, 16 (2), 149-161. (21) Chua, H. T.; Ng, K. C.; Malek, A.; Kashiwagi, T.; Akisawa, A.; Saha, B. B. Modeling the performance of two-bed, silica gel-water adsorption chillers. Int. J. Refrig. 1998, 22, 194-204.
Figure 3. Specific heat capacities of a Maxsorb charcoal + HFC134a system. When adsorption temperature is 273 K: (O) the newly interpreted specific heat capacity; (9) the specific heat capacity of the adsorbent + adsorbate system by assuming a gas phase adsorbate; (4) the specific heat capacity of the system by assuming a liquid phase adsorbate. When adsorption temperature is 353 K: (b) the newly interpreted specific heat capacity; (0) the specific heat capacity of the adsorbent + adsorbate system by assuming a gas phase adsorbate (2) the specific heat capacity of the system by assuming a liquid phase adsorbate.
becomes more ideal. For activated charcoal + HFC134a systems, out of the three types of activated charcoal which Akkimaradi et al.15 reported, the maximum ∆cp for Chemviron activated charcoal is about 6% and that for Fluka activated charcoal is about 12%. These deviations occur at the 273 K isotherms. Figure 3 shows the plot of cas, cgs, and cls of Maxsorb activated charcoal, which Akkimaradi et al. also investigated, at 353 and 273 K, respectively. One could observe that cls is consistently higher than cas and cgs, and the correction offered by cas could be as high as 38% at 273 K. Figure 4 shows the plot of specific heat capacities of the activated carbon + nitrogen system at the temperatures 150 and 390 K, respectively, where ∆cp is very significant. At 150 K, the value ∆cp ranges from 5% to 14%, but at 390 K or the high-temperature isotherm, the value ∆cp decreases to about 0.4%. The specific heat capacities of activated carbon + hydrogen at the temperatures 77 and 190 K are plotted against pressures in Figure 5. ∆cp (up to 4%) is significant at the low-temperature isotherm 77 K, but at 190 K the value ∆cp becomes nearly zero. The newly proposed form of the specific heat capacity and the conventionally used form of specific heat capacities of an activated carbon + neon system are plotted in Figure 6. The value ∆cp varies
Adsorbate-Adsorbent System
Figure 4. Specific heat capacities of an activated charcoal + nitrogen system. When adsorption isotherm temperature is 150 K: (2) the newly interpreted specific heat capacity; (0) the specific heat capacity of the adsorbent + adsorbate system by assuming a gas phase adsorbate. When adsorption temperature is 390 K: (O) the newly interpreted specific heat capacity; (9) the specific heat capacity of the system by assuming a gas phase adsorbate.
Langmuir, Vol. 19, No. 6, 2003 2259
Figure 6. Specific heat capacities of an activated charcoal + neon system. When adsorption temperature is 77 K: (2) the newly interpreted specific heat capacity; (0) the specific heat capacity of the adsorbent + adsorbate system by assuming a gas phase adsorbate. When adsorption temperature is 190 K: (the thick line) the newly interpreted specific heat capacity; (the dotted line) the specific heat capacity of the system by assuming a gas phase adsorbate.
of Jose et al.22 so as to arrive at an improved understanding of the thermal diffusivity of the system when the system volume does not change significantly during the adsorption/desorption process. Conclusion
Figure 5. Specific heat capacities of an activated charcoal + hydrogen system. When adsorption temperature is 77 K: (4) the newly interpreted specific heat capacity; (9) the specific heat capacity of the adsorbent + adsorbate system by assuming a gas phase adsorbate. When adsorption temperature is 190 K: (O) the newly interpreted specific heat capacity; (the thick line) the specific heat capacity of the system by assuming a gas phase adsorbate.
from 5% to 14% with pressure (from 0.3 to 0.8 MPa) at low temperature (77 K), but at 190 K, ∆cp is nearly equal to zero. Our newly interpreted specific heat capacity expression for the single-component adsorbent + adsorbate system should complement the thermal conductivity expression
The formulations of thermodynamic property fields, namely specific heat capacity, internal energy, enthalpy, and entropy of a single-component adsorbent + adsorbate system, are the basic foundations of any adsorbateadsorbent system. Such key thermodynamic quantities are essential in the development of adsorption thermodynamics, and they would be useful in the design and analysis of solid-gas sorption in the cooling sector such as the adsorption cooling cycle, adsorption cryocoolers, and cooling infrared detectors. It has been shown that the error made in earlier expressions of specific heat capacities can be significant at high pressures and lower temperatures especially for large adsorbate molecules that are of practical interest. Furthermore, the partial enthalpy and entropy can be evaluated at (1) the prevailing temperature and (2) the saturated pressure that are commensurate with the prevailing temperature and uptake. LA0267140 (22) Prakash, M. J.; Prasad, M.; Srinivasan, K. Modeling of thermal conductivity of charcoal-nitrogen adsorption beds. Carbon 2000, 38 (6), 907-913.
