^{1,a)}, Yong Zhou (周永)

^{1}and Eric W. Lemmon

^{2}

### Abstract

A thermodynamic property formulation for dimethyl ether has been developed based on a selection of experimental thermodynamic property data. The formulation includes a fundamental equation, a vapor-pressure equation, and saturated-density equations for liquid and vapor states. In determining the coefficients of the equation of state, multiproperty fitting methods were used that included single-phase pressure-density-temperature , heat capacity,vapor pressure, and saturated density data. Deviations between experimental and calculated data are generally within the experimental accuracy. The equation of state has been developed to conform to the Maxwell criterion for two-phase liquid-vapor equilibrium states, and is valid for temperatures from the triple-point temperature to , with pressures up to and densities up to . The uncertainties of the equation of state in density are 0.1% for the liquid phase and 0.3% for the vapor phase. In the extended critical region, the uncertainties in density are 0.5%, except for very near the critical point. The uncertainties in vapor pressure are 0.2% above , and increase as temperature decreases. The uncertainties in saturated liquid density are 0.05%, except for near the critical point. The uncertainties in heat capacity are 2.0%. Detailed comparisons between the experimental data and calculated values are given.

This research is supported by the Foundation for the National Natural Science Foundation of China (Grant No. 51076128), the National High Technology Research and Development Program of China (Grant No. 2009AA05Z107), and the Fok Ying Tung Education Foundation (Project No. 111060).

1. Introduction

2. Critical and Triple Parameters of Dimethyl Ether

3. Auxiliary Equations

3.1. The vapor-pressure equation

3.2. The saturated-liquid density equation

3.3. The saturated-vapor density equation

4. The Equation of State

4.1. Ideal-gas Helmholtz energy

4.2. Residual Helmholtz energy

4.3. Comparisons with experimental data

4.3.1. Comparisons with saturation thermal data

4.3.2. Comparisons with data and virial coefficients

4.3.3. Comparisons with caloric data

4.4. The extrapolation behavior of the equation of state

5. Conclusions

### Key Topics

- Equations of state
- 67.0
- Heat capacity
- 23.0
- Vapor pressure
- 17.0
- Maxwell equations
- 10.0
- Thermodynamic properties
- 8.0

## Figures

Reported critical temperatures of dimethyl ether as a function of the year published.

Reported critical temperatures of dimethyl ether as a function of the year published.

Reported critical densities of dimethyl ether as a function of the year published.

Reported critical densities of dimethyl ether as a function of the year published.

Reported critical pressures of dimethyl ether as a function of the year published.

Reported critical pressures of dimethyl ether as a function of the year published.

Comparisons of ideal gas heat capacities calculated with Eq. (7) to experimental and theoretical data as a function of temperature.

Comparisons of ideal gas heat capacities calculated with Eq. (7) to experimental and theoretical data as a function of temperature.

Comparisons of vapor pressures calculated with the equation of state to experimental data as a function of temperature (the range of the -axis is ). The solid line corresponds to values calculated from the ancillary equation, Eq. (1). The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of vapor pressures calculated with the equation of state to experimental data as a function of temperature (the range of the -axis is ). The solid line corresponds to values calculated from the ancillary equation, Eq. (1). The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of vapor pressures calculated with the equation of state to experimental data as a function of temperature (the range of the -axis is ). The line corresponds to values calculated from the ancillary equation, Eq. (1). The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of vapor pressures calculated with the equation of state to experimental data as a function of temperature (the range of the -axis is ). The line corresponds to values calculated from the ancillary equation, Eq. (1). The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of saturated liquid densities calculated with the equation of state to experimental data as a function of temperature. The line corresponds to values calculated from the ancillary equation, Eq. (2). The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of saturated liquid densities calculated with the equation of state to experimental data as a function of temperature. The line corresponds to values calculated from the ancillary equation, Eq. (2). The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of saturated vapor densities calculated with the equation of state to experimental data as a function of temperature. The line corresponds to values calculated from the ancillary equation, Eq. (3). The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of saturated vapor densities calculated with the equation of state to experimental data as a function of temperature. The line corresponds to values calculated from the ancillary equation, Eq. (3). The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Experimetal data as a function of temperature and pressure.

Experimetal data as a function of temperature and pressure.

Comparisons of densities calculated with the equation of state to experimental data as a function of pressure. The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of densities calculated with the equation of state to experimental data as a function of pressure. The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparison of second virial coefficients *B* calculated with the equation of state to experimental data as a function of temperature. The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparison of second virial coefficients *B* calculated with the equation of state to experimental data as a function of temperature. The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparison of third virial coefficients *C* calculated with the equation of state to experimental data as a function of temperature. The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparison of third virial coefficients *C* calculated with the equation of state to experimental data as a function of temperature. The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Calculations of along isotherms versus density in the vapor-phase region and two-phase region. Isotherms are shown at temperatures of 220, 240, 260, 280, 300, 400.378, 500, 600, 700, 800, 900, and .

Calculations of along isotherms versus density in the vapor-phase region and two-phase region. Isotherms are shown at temperatures of 220, 240, 260, 280, 300, 400.378, 500, 600, 700, 800, 900, and .

Experimental caloric data as a function of temperature and pressure.

Experimental caloric data as a function of temperature and pressure.

Comparisons of saturation heat capacities calculated with the equation of state to experimental data as a function of temperature. The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of saturation heat capacities calculated with the equation of state to experimental data as a function of temperature. The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of two-phase isochoric heat capacities calculated with the equation of state to experimental data as a function of temperature. The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of two-phase isochoric heat capacities calculated with the equation of state to experimental data as a function of temperature. The dashed line corresponds to values calculated from the equation of state of Ihmels and Lemmon.^{12}

Comparisons of isobaric heat capacities calculated with the equation of state to experimental data as a function of temperature.

Comparisons of isobaric heat capacities calculated with the equation of state to experimental data as a function of temperature.

Comparisons of isochoric heat capacities calculated with the equation of state to experimental data as a function of temperature.

Comparisons of isochoric heat capacities calculated with the equation of state to experimental data as a function of temperature.

Isochoric heat capacity versus temperature. Isobars are shown at pressures of 0, 0.1, 0.5, 1, 2, 3, 4, 5, 6, 8, 10, 20, 50, 100, 200, 500, 1000, 2000, and . The dashed line and the dotted line are shown at the triple-point temperature and the critical-point temperature , respectively.

Isochoric heat capacity versus temperature. Isobars are shown at pressures of 0, 0.1, 0.5, 1, 2, 3, 4, 5, 6, 8, 10, 20, 50, 100, 200, 500, 1000, 2000, and . The dashed line and the dotted line are shown at the triple-point temperature and the critical-point temperature , respectively.

Isobaric heat capacity versus temperature. Isobars are shown at pressures of 0, 0.1, 0.5, 1, 2, 3, 4, 5, 6, 8, 10, 20, 50, 100, 200, 500, 1000, 2000, and . The dashed line and the dotted line are shown at the triple-point temperature and the critical-point temperature , respectively.

Isobaric heat capacity versus temperature. Isobars are shown at pressures of 0, 0.1, 0.5, 1, 2, 3, 4, 5, 6, 8, 10, 20, 50, 100, 200, 500, 1000, 2000, and . The dashed line and the dotted line are shown at the triple-point temperature and the critical-point temperature , respectively.

Sound speed *w* versus temperature. Isobars are shown at pressures of 0, 0.1, 0.5, 1, 2, 3, 4, 5, 6, 8, 10, 20, 50, 100, 200, 500, 1000, 2000, and . The dashed line and the dotted line are shown at the triple-point temperature and the critical-point temperature , respectively.

Sound speed *w* versus temperature. Isobars are shown at pressures of 0, 0.1, 0.5, 1, 2, 3, 4, 5, 6, 8, 10, 20, 50, 100, 200, 500, 1000, 2000, and . The dashed line and the dotted line are shown at the triple-point temperature and the critical-point temperature , respectively.

Isobaric behavior of the equation of state for dimethyl ether. Isobars are shown at pressures of 0.1, 0.2, 0.5, 1, 2, , 10, 20, 50, 100, 200, 500, and . The rectilinear diameter is shown in the diagram.

Isobaric behavior of the equation of state for dimethyl ether. Isobars are shown at pressures of 0.1, 0.2, 0.5, 1, 2, , 10, 20, 50, 100, 200, 500, and . The rectilinear diameter is shown in the diagram.

Isothermal behavior of the equation of state at extreme conditions of temperature and pressure. Isotherms are shown at temperatures of , 150, 200, 250, 300, 350, , 500, 1000, 5000, 10 000, 50 000, 100 000, 500 000, and .

Isothermal behavior of the equation of state at extreme conditions of temperature and pressure. Isotherms are shown at temperatures of , 150, 200, 250, 300, 350, , 500, 1000, 5000, 10 000, 50 000, 100 000, 500 000, and .

Characteristic (ideal) curves of the equation of state as a function of reduced temperature and reduced pressure .

Characteristic (ideal) curves of the equation of state as a function of reduced temperature and reduced pressure .

## Tables

Physical constants and characteristic properties of dimethyl ether

Physical constants and characteristic properties of dimethyl ether

Published critical parameters of dimethyl ether

Published critical parameters of dimethyl ether

Summary of vapor-pressure data for dimethyl ether

Summary of vapor-pressure data for dimethyl ether

Summary of saturated-liquid density data for dimethyl ether

Summary of saturated-liquid density data for dimethyl ether

Summary of saturated-vapor density data for dimethyl ether

Summary of saturated-vapor density data for dimethyl ether

Summary of and virial-coefficient data for dimethyl ether

Summary of and virial-coefficient data for dimethyl ether

Summary of caloric data for dimethyl ether

Summary of caloric data for dimethyl ether

The coefficients and exponents of the equation of state

The coefficients and exponents of the equation of state

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