Question

The specific volume of saturated steam can be calculate using the ideal gas equation of state and the saturation temperature and pressure as follows $\frac{RT_{sat}(P)}{P}$ where $v_g$= specific volume of saturated steam [units kg/m³] P = Pressure [units Pa] $T_{sat}(P)$ = Saturation temperature at pressure P [units K] R = specific ideal gas constant (= 461.5 J/kg K for steam) It is well known, however, that the ideal gas equation will produce very large errors at high pressure, in particular as the pressure approaches the critical point. Affandi et al. (2013) have proposed an alternative equation of state, based on the reduced saturation temperature ($T_r = T/T_{crit}$) only, as follows $\ln(v_g) = a + b[\ln(1/T_r)]^{0.4} + c/T_r^2 + d/T_r^4 + e/T_r^5$ Values for a-e are given in the table below a b c d e -7.75883 3.23753 2.05755 -0.06052 0.00529 The aim of this exercise is to validate or otherwise the two methods using a data set taken from the Rogers and Mayhew property tables used in this module. a. Write a function to calculate the specific volume using the ideal gas equation. The input of the function should be temperature (in units of degrees Celsius). The output should be in units of m³/kg. b. Write a function to calculate the specific volume using the Affandi Equation. The input of the function should be temperature (in units of degrees Celsius). The output should be in units of m³/kg.

          The specific volume of saturated steam can be calculate using the ideal gas equation of state and the
saturation temperature and pressure as follows
$\frac{RT_{sat}(P)}{P}$
where
$v_g$= specific volume of saturated steam [units kg/m³]
P = Pressure [units Pa]
$T_{sat}(P)$ = Saturation temperature at pressure P [units K]
R = specific ideal gas constant (= 461.5 J/kg K for steam)
It is well known, however, that the ideal gas equation will produce very large errors at high pressure,
in particular as the pressure approaches the critical point.
Affandi et al. (2013) have proposed an alternative equation of state, based on the reduced
saturation temperature ($T_r = T/T_{crit}$) only, as follows
$\ln(v_g) = a + b[\ln(1/T_r)]^{0.4} + c/T_r^2 + d/T_r^4 + e/T_r^5$
Values for a-e are given in the table below
a	b	c	d	e
-7.75883	3.23753	2.05755	-0.06052	0.00529
The aim of this exercise is to validate or otherwise the two methods using a data set taken from the
Rogers and Mayhew property tables used in this module.
a. Write a function to calculate the specific volume using the ideal gas equation. The
input of the function should be temperature (in units of degrees Celsius). The output
should be in units of m³/kg.
b. Write a function to calculate the specific volume using the Affandi Equation. The
input of the function should be temperature (in units of degrees Celsius). The output
should be in units of m³/kg.

The specific volume of saturated steam can be calculate using the ideal gas equation of state and the
saturation temperature and pressure as follows
(RTsat(P))/(P)
where
vg= specific volume of saturated steam [units kg/m³]
P = Pressure [units Pa]
Tsat(P) = Saturation temperature at pressure P [units K]
R = specific ideal gas constant (= 461.5 J/kg K for steam)
It is well known, however, that the ideal gas equation will produce very large errors at high pressure,
in particular as the pressure approaches the critical point.
Affandi et al. (2013) have proposed an alternative equation of state, based on the reduced
saturation temperature (Tr = T/Tcrit) only, as follows
ln(vg) = a + b[ln(1/Tr)]^0.4 + c/Tr^2 + d/Tr^4 + e/Tr^5
Values for a-e are given in the table below
a b c d e
-7.75883 3.23753 2.05755 -0.06052 0.00529
The aim of this exercise is to validate or otherwise the two methods using a data set taken from the
Rogers and Mayhew property tables used in this module.
a. Write a function to calculate the specific volume using the ideal gas equation. The
input of the function should be temperature (in units of degrees Celsius). The output
should be in units of m³/kg.
b. Write a function to calculate the specific volume using the Affandi Equation. The
input of the function should be temperature (in units of degrees Celsius). The output
should be in units of m³/kg.

Added by Shari M.

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