NEW RELATION BETWEEN VOLUME THERMAL EXPANSION AND THERMAL PRESSURE FOR SOLIDS

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1 NEW RELATION BETWEEN VOLUME THERMAL EXANSION AND THERMAL RESSURE FOR SOLIDS Sumiti Narayan Tewari 1, Anita Shukla 1, Department of hysics, ranveer Singh Institute of Technology, Bhauti, Kanpur 8 U.. (India) ABSTRACT A new relation between volume ermal expansion and ermal pressure for NaCl, KCl, MgO, CaO, Al O, and Mg SiO 4 has been derived. The results from is relation have been compared wi experimental data and e results obtained by Kushwah et.al.. It has been observed at e new relation is in close agreement wi experimental data. Keywords: Equation of State; Bulk Modulus; Thermal ressure; Thermal Expansion. I INTRODUCTION Volume expansion of solids due to rise in temperature is directly related to ermal pressure 1,. Anderson gave a relation for ermal pressure as V T V, T, (1) where V is e volume, T e temperature and T is initial value of temperature taken here is equal to K. The last term in Equation (1) represents e difference in values of ermal pressure at two temperatures T and T. i.e. T () T In Equation (1) and (), it has been assumed at e ermal pressure is a function of temperature only. At atmospheric pressure, i.e. at (V, T) =, we have: V T, () 195 a g e

2 II. METHOD OF ANALYSIS The generalized Kushwah logarimic EOS can be written as 4 K ' 1 x A ln1 x A ln1 x A ln1 x 1 (4) where x = (1 V/V ), V is e volume at atmospheric pressure, e constants A 1, A, and A are defined by Kushwah et al 5. as A1 K (5) ' K K 1 1 A (6) K ' K' A 1 K (7) 5 5 where K and K are isoermal bulk modulus and its first derivative at zero atmospheric pressure. Values of K and K for NaCl, KCl, MgO, CaO, Al O, and Mg SiO 4 are given in Table 1. Table 1- Values of input data used in calculations, isoermal bulk modulus K (Ga) and pressure derivative of isoermal bulk modulus K are at T = K and atmospheric pressure 5. K K K NaCl KCl MgO CaO Al O Mg SiO From Equation () and (4) i.e. difference in ermal pressure can be obtained as K ' 1 x A ln1 x A ln1 x A ln1 x 1 (8) Here V/V is e volume expansion wi increase in temperature for solids at atmospheric pressure ( = ) We suggest a new relation for for solids as V / V B B1Exp (9) B 196 a g e

3 where B, B 1, and B are constants and values of ese constants are given in table and obtained values of ermal pressure and volume ermal expansion V/V for NaCl, KCl, MgO, CaO, Al O, and Mg SiO 4 as a function of temperature as given in Table. Table ----Values of constants B, B 1, and B for NaCl, KCl, MgO, CaO, Al O, and Mg SiO 4 obtained from mat lab. B B 1 B NaCl KCl MgO CaO Al O Mg SiO Table --- values of ermal pressure MgO, CaO, Al O, and Mg SiO 4 as a function of temperature. and volume ermal expansion V/V for NaCl, KCl, (Ga) Volume ermal expansion V/V Ref [] 197 a g e (Ga) Eq. (8) Ref. [] NaCl KCl

4 Table values of ermal pressure MgO, CaO, Al O, and Mg SiO 4 as a function of temperature and volume ermal expansion V/V for NaCl, KCl, (Ga) Eq. (8) Ref. [] Volume ermal expansion V/V Ref [] MgO (Ga) CaO Al O a g e

5 Table values of ermal pressure and volume ermal expansion V/V for NaCl, KCl, MgO, CaO, Al O, and Mg SiO 4 as a function of temperature (Ga) Volume ermal expansion V/V Ref [] Eq. (8) Ref. [] Mg SiO (Ga) III. CONCLUSION Comparison of difference in ermal pressure wi respect to volume expansion for NaCl, KCl, MgO, CaO, Al O, and Mg SiO 4 is given in Table. Which show at values of predicted from Equation (9) is accurate and close to experimental data as compared to Equation (8) proposed by Kushwah et al. REFRENCES 1 Kushwah S S & Shanker J, hysica B, 5, 1998, 9. Shanker J & Kushwah S S, High High pressure,, 1, 7. Anderson O L, Equation of state of solids for geophysics and ceramic science, (Oxford University ress, New York), Kushwah S S, Shrivastava H C & Singh K S, hysica B, 88,7,. 5 Kushwah S S & Tomar Y S, Indian Journal of ure and Applied hysics, 49,11, a g e