### Mathematical Model Simulation of Non-Linear Equations using MATLAB: Specific Volume of Gas with Van der Waals Equation

Ayu Fitri Amalia, Widodo Budhi, Asih Melati, Urip Nurwijayanto Prabowo

#### Abstract

Computational physics is concerned with the application of numerical methods in solving physical problems. The van der Waals gas model is one of the most common non-linear models. This study simulated a mathematical model of a non-linear equation using MatLab for the case of the specific volume of gas in the equation of the state of van der Waals. This study aimed to determine the molar volume and compressibility factor, as well as describe the relationship between the compressibility factor and the reduced pressure. The method of the study is experimental. The independent variables are the reduced pressure and temperature values. The dependent variable is the determination of the value of the molar volume (V) and the compressibility factor (Z). The control variable, in the form of a function used in solving this case, is based on van der Waals equation with the gas used is ammonia. The fzero command can be used to solve f(x)=0 with a single variable. This program that has been running successfully can show various predictions in the form of reduction pressure, thus obtaining the values of the molar volume and compressibility factor using the ideal gas equation. There is a deviation in ammonia gas, the Z>1 at high reduction pressures and Z<1 at medium pressures. This study can provide contributions and benefits in the form of material enrichment of thermodynamics to understand how real gases behave. The ideal gas equation can be modified into the van der Waals equation.

#### Keywords

MatLab; Non-Linear Equation; Specific Volume of Gas; Van der Waals Equation;

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DOI: http://dx.doi.org/10.24042/jipfalbiruni.v11i2.12546

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