Find the temperature (in degrees Celsius) of methane (CH4) at a pressure p = 101.3 kPa and specific volume v = 0.54997 m^3/kg using the Lee-Kesler equation of state. Solve the equation using your Modified Regula Falsi program.
The Lee-Kesler equation of state is given by:
P = exp((2.18 * (1 + (0.5 * 0.1181493 * (1 - (0.265728 / Tr^0.15479))^2 / (0.030323 * (1 - (0.023674 / Tr^0.016698))^2)) / Tr^2)) * (Tr / (1 + (0.155408 / Tr^0.623689) + (0.65392 / Tr^0.060167)^3)))
Where:
P is the pressure in MPa
Tr is the reduced temperature (T / Tc)
Tc is the critical temperature of methane (-82.59°C)
Note that:
Tr, P, and v are dimensionless. Absolute pressures and temperatures must be used (K = °C + 273.15). The gas constant R = R/M, where the universal gas constant R = 8.31434 kJ/kmol·K and the molecular weight of methane is M = 16.0425 kg/kmol. The critical constants for methane are Pc = 4.5992 MPa and Tc = -82.59°C.
Please submit the following:
1. A plot which shows the location of all real roots T of the equation for the given values of p and v.
2. A flow chart of the Modified Regula Falsi algorithm.
3. Your Matlab main program and all function programs used.
4. Printed output from your program showing the computed value of T to an accuracy of at least 6 significant figures.
5. The calculated value of the temperature T (in degrees Celsius) using the Lee-Kesler equation of state and the relative error compared to the ideal gas (-161.45°C). Present each value reported in methane property tables with at least 6 significant figures in your results.