2023: Volume 5, Issue 2
Past Issues
Abstract 
PDFThe Isochoric Heat Capacity of Ice is Equal to its Isobaric Heat Capacity
Igor A Stepanov*
Institute of Science and Innovative Technologies, Liepaja University, Liela 14, Liepaja, LV-3401, Latvia
*Corresponding Author: Igor A Stepanov, Institute of Science and Innovative Technologies, Liepaja University, Liela 14, Liepaja, LV-3401, Latvia; Fax: +371 634 23568; E-mail: [email protected]
Received Date: October 11, 2023
Publication Date: October 26, 2023
Citation: Stepanov IA, et al. (2023). The Isochoric Heat Capacity of Ice is Equal to its Isobaric Heat Capacity. Material Science. 5(2):21.
Copyright: Stepanov IA, et al. © (2023).
ABSTRACT
Formerly the author theoretically obtained the result that the isochoric heat capacity is equal to the isobaric heat capacity. In the present paper this conclusion is compared with experimental results for H2O ice Ih. A sound agreement between the theory and experiment is observed.
Keywords: Reech’s relation; Ice; generalized Mayer's relation; Heat capacity; isothermal compressibility; adiabatic compressibility; the First law of thermodynamics
INTRODUCTION
In [1] the author developed a theory that the isochoric heat capacity CV is equal to the isobaric heat capacity CP. It is necessary to confirm that conclusion with experimental results. Relevant experimental results for H2O Ice Ih were published in [2] and using them one can check the theoretical results of [1].
THEORY
The first law of thermodynamics for the heat exchange can be written like this in its traditional form:
Here dQ is the heat introduced into the system. It is an exact differential because pressure is constant.
In [1] it was shown that this law must have the following form
Pay attention that dQ is an exact differential. For a constant pressure, Eq. 2 turns to Eq. 1, and for a constant volume, Eq. 2 turns to the following equation:
The traditional heat capacities CP and CV are obtained from Eq. 1.
There is Reech’s relation [3,4]:
Here KT and KS are isothermal and adiabatic compressibility, respectively. In the derivation of Reech’s relation only reciprocity theorem is used [4] and this derivation is independent of a form of the first law of thermodynamics: Eqs. 1 or 2.
In [2] numerous values of KT and KS for water Ice Ih were presented: Table 1.
Table 1: Isothermal compressibility KT, and adiabatic compressibility KS, for ice Ih [2]a
|
T,K |
KT,10-10Pa-1 |
KS,10-10 Pa-1 |
g, Eq. 4 |
|
0 |
0.8825 |
0.8825 |
1,0000 |
|
10 |
0.8880 |
0.8880 |
1.0000 |
|
20 |
0.8936 |
0.8935 |
1.0001 |
|
30 |
0.8992 |
0.8990 |
1.0002 |
|
40 |
0.9049 |
0.9047 |
1.0002 |
|
50 |
0.9094 |
0.9093 |
1.0001 |
|
60 |
0.9160 |
0.9160 |
1.0000 |
|
70 |
0.9229 |
0.9228 |
1.0001 |
|
80 |
0.9304 |
0.9301 |
1.0003 |
|
90 |
0.9384 |
0.9376 |
1.0009 |
|
100 |
0.9471 |
0.9456 |
1.0016 |
|
110 |
0.956 |
0.9539 |
1.0022 |
|
120 |
0.9660 |
0.9626 |
1.0035 |
|
130 |
0.9768 |
0.9717 |
1.0053 |
|
140 |
0.9880 |
0.9813 |
1.0068 |
|
150 |
0.9997 |
0.9913 |
1.0085 |
|
160 |
1.012 |
1.002 |
1.0100 |
|
170 |
1.026 |
1.013 |
1.0128 |
|
180 |
1.039 |
1.024 |
1.0147 |
|
190 |
1.054 |
1.036 |
1.0174 |
|
200 |
1.069 |
1.049 |
1.0191 |
|
210 |
1.085 |
1.062 |
1.0217 |
|
220 |
1.102 |
1.076 |
1.0242 |
|
230 |
1.119 |
1.091 |
1.0257 |
|
240 |
1.137 |
1.106 |
1.0280 |
|
250 |
1.155 |
1.122 |
1.0294 |
|
260 |
1.139 |
1.173 |
0.9710 |
|
270 |
1.191 |
1.157 |
1.0294 |
|
273 |
1.196 |
1.162 |
1,0293 |
aThe uncertainties for KS, and KT are ±1.3%, and ±1.5%, respectively.
DISCUSSIONS AND CONCLUSIONS
The data presented in Table 1 provide good evidence that Eq. 2 formerly obtained by the author is correct. However, further research is needed to prove that finally. These data confirm well the result obtained buy A. Guy: |PDV|=|VDP| [1]. Also it is necessary to note that according to [5] the first law of thermodynamics for the heat exchange for substances with negative thermal expansion has the following form:
This form differs from that in Eq. 1. In [5] it was shown using experimental data that for substances with negative thermal expansion CV > CP and KS > KT. It means that the traditional result CP > CV and KT > KS is not that undoubtful. In Table 1 for T = 260 K, formally KS > KT.
STATEMENTS AND DECLARATIONS
Competing Interests
The author has no competing interests to declare that are relevant to the content of this article.
The author has no relevant financial or non-financial interests to disclose. There was no Funding of the manuscript.
Data Availability Statement (DAS)
The data used to generate the results in the paper are available in the paper.
REFERENCES
- Stepanov IA. (2017). Exact calculation of the internal energy of the ideal gas in statistical mechanics. Phy Sci International J. 14(2):1. Free online
- Neumeier JJ. (2018). Elastic Constants, Bulk Modulus, and Compressibility of H2O Ice Ih for the Temperature Range
- 50 K–273 K. J Phys Chem. Ref. Data. 47(3):033101.
- Guemez J, Fiolhais C, Fiolhais M. (1999). Thermodynamics at work: The pressure derivative of the specific heat. Am J Phys. 67(12):1100.
- Adkins CJ. (1983). Equilibrium Thermodynamics. Cambridge University Press, Cambridge:115.
- Stepanov IA. (2016). The isochoric heat capacity of ZrW2O8 and Sc2W3O12 is greater than their isobaric one. Mater Lett. 177:112.
