Temperature Dependent Equation of State for Solids

Abstract

The temperature dependent equation of state (EOS) is developed in the present work to analyze the thermo-elastic properties of solids. The new EOS is formulated by modifying the pressure dependent form of EOS reported recently by the present authors to explain the elastic behavior of nanomaterials. The values of thermal expansion are calculated for NaCl as an example using the newly formulation under varying temperature conditions from 298 K -773K and compared with the available experimental data. An excellent agreement is obtained between the calculated results and the experimental data. The model is extended for the study of bulk modulus and thermal expansion coefficient of NaCl over the temperature range 298 K to 773K. The results so calculated are found in close agreement with the experimental data. Further the model is applied to study the volume compression in NaCl solid over the pressure ranging from 0 to 30 GPa at different isotherms. The calculated values of compression are achieved in excellent agreement with the experimental data. The present model theory is thus applicable to explain the thermo-elastic properties of solids satisfactorily under high temperature and high pressure.

Modelling for the Study of Thermoelastic Properties of Nanoparticles

“…Thus, we can conclude that when we incorporated the concepts suggested by Qi [9] into model proposed by Goyal et. al., [6] and Kumar et. al., [8], we found better results.…”

Melting Is Well-Known, but Is It Also Well-Understood?

“…As a last example of an EoS approach, we refer to the model of Goyal and Gupta. , Their EoS is given by P false( V , T 0 false) = K 0 false( η − 1 − 1 false) + false( 1 / 2 false) K 0 false( K 0 ′ − 1 false) ( η − 1 − 1 ) 2 where η = V / V 0 , K 0 = − V (∂ P /∂ V ) T , and K 0 ′ = ∂( K 0 /∂ P ) T and the subscript “0” indicates that the values are calculated at P = 0, while T 0 denotes room temperature. This equation can be easily inverted and yields imaginary values for η above a certain temperature, which is identified as T mel . Further, P ( V , T 0 ) can be replaced by P ( V , T ) – P the , where the thermal pressure P the is calculated from P the = ∫ T 0 T αK d T with as usual α the thermal expansivity.…”