Investigation of the Pressure Derivative of Partition Function on Thermodynamic Properties of Hydrogen Thermal Plasma in Local Thermodynamic Equilibrium

In the present work, thermodynamic properties such as compressibility coefficient, adiabatic coefficient, specific heat at constant volume, isentropic coefficient, and sound speed of hydrogen thermal plasma in local thermodynamic equilibrium (LTE) conditions have been investigated in the temperature range from 5000K to 50000K at different pressures of 1 atm, 100 atm, and 1000 atm. Two cases have been considered: (i) when the expressions include the pressure derivative of the partition function, and (ii) when the pressure derivative of the partition function is excluded from expressions. It has been observed that the temperature from which the pressure derivative starts influencing a given thermodynamic property increases with the increase in pressure. The thermodynamic property for case (i) is always greater than its value for case (ii) for compressibility coefficient and specific heat at constant volume, while the reverse is true for adiabatic coefficient, isentropic coefficient, and sound speed. The relationship of the compressibility coefficient with the degree of ionisation does depend upon pressure in the case (i), whereas it is independent of pressure in the case (ii). The relative deviation between the two cases increases with augmentation of pressure for the compressibility coefficient, specific heat at constant volume, and adiabatic coefficient, such that their maximum values are large, whereas for the isentropic coefficient and sound speed, it is marginal even at high values of pressure.