MATHEMATICAL AND NUMERICAL ANALYSIS OF THE RELATIONSHIP AMONG THE LOSCHMIDT CONSTANT, THE AVOGADRO CONSTANT, AND THE SPEED OF SOUND IN IDEAL AND REAL GASES AT STANDARD STATE
<p>In this paper, a differential equation is derived relating to the relationship among the Loschmidt constant, the Avogadro constant, and the speed of sound in gases as a function of the thermodynamic properties of the gas (pressure, temperature, and volume). To confirm the validity of the derived equation, the ratio of the constants NL/NA and the deviation of the NL/NA ratio for several ideal gases (hydrogen, helium, carbon monoxide,<br />nitrogen, oxygen, carbon dioxide, methane) were calculated using the ideal-gas equations of state (Pv=RT). The calculation of the ratio of the constants NL/NA and the deviation of the NL/NA ratio from the value for the gases at standard state (i.e., temperature 273.15 K and pressure 101325 Pa) is in a good agreement with the results published in literature, given the fact that the literature data of the NL/NA ratio is 0.04461498 at standard state. As the second step in confirming the validity of the derived equation, the ratio of the constants NL/NA and the deviation of the NL/NA ratio for several real gases (hydrogen, helium, carbon monoxide, nitrogen, oxygen, carbon dioxide, methane) were calculated using the real-gas Van der Waals equation of state. In this case, the calculation results are also in agreement with the reference value.</p>