Joule coefficient

The results of early experiments showed that the temperature did not change on the expansion of the gas, and consequently the value of the Joule coefficient was zero. The heat capacity of the gas is finite and nonzero. Therefore, it was concluded that (dE/dV)Tn was zero. Later and more-precise experiments have shown that the Joule coefficient is not zero for real gases, and therefore (dE/dV)Ttheoretical concepts of the ideal gas. 

The Joule effect is discussed in Section 2.8 in conjunction with the definition of an ideal gas. When Equations (2.40) and (4.64) are combined, the expression for the Joule coefficient becomes. 

We conclude from Equation (7.41) that the Joule coefficient is a function of both the temperature and the volume. Moreover, the value of the coefficient goes to zero as the molar volume approaches infinity. 

We conclude that the Joule-Thomson coefficient is a function of both the temperature and the pressure, but, unlike the Joule coefficient, it does not go to zero as the pressure goes to zero. The inversion temperature, the temperature at which fi,T = 0, is also a function of the pressure. The value usually reported in the literature is the limiting value as the pressure goes to zero. 

Show that the Joule coefficient can he obtained from the equation of state of a gas... 

This quantity is called the Joule coefficient. It is the limit of -(A77AF) . corrected for the heat capacity of the containers as AUapproaches zero. With the van der Waals equation of state, we obtain p = ajy C - The eorrected temperature change when the two eontain-ers are of equal volume is found by integration to be AT = -a/2 FC , where V is the initial molar volume and C is the molar constant-volume heat capacity. It is instractive to calculate this AT for a gas such as CO2. In addition, the student may consider the relative heat capacities of 10 L of the gas at a pressure of 1 bar and that of the quantity of eopper required to constract two spheres of this volume with walls (say) 1 mm thiek and then eal-culate the AT expected to be observed with such an experimental arrangement. 

The quantity dT/dV)u is called the Joule coefficient. James Joule attempted to evaluate this quantity by measuring the temperature change accompanying the expansion of air into a vacuum—the Joule experiment. Write an expression for the total differential of U with T and V as independent variables, and by a procedure similar to that used in Sec. 7.5.2 show that the Joule coefficient is equal to... 

The Joule experiment was carried out several times with various volumes for the second chamber. The ratio AT/AV would be determined for each experiment and extrapolated to zero value of A V, where A V is the final volume of the gas minus its initial volume. This extrapolation is equivalent to taking the mathematical limit, so the result is a partial derivative, called the Joule coefficient and denoted by /uj ... 

Joule was unsuccessful in his attempt to measure the Joule coefficient because the changes in temperature that occurred were too small to be measured by his thermometers, even though he used pressures up to 22 atm. Later versions of the experiment with better apparatus have given nonzero values of (dU/dV)T for real... 

Buckingham R A and Corner J 1947 Tables of second virial and low-pressure Joule-Thompson coefficients for intermolecular potentials with exponential repulsion Proc. R. Soc. A 189 118... 

At constant pressure L Joule-Thomson coefficient fX, fXjT-... 

The coefficient k, expressed in J sec cm is the quantity of heat in joules, transmitted per second through a sample one centimeter in thickness and one square centimeter in area when the temperature difference between the two sides is one degree kelvin (or Celsius). The tabulated values are in microjoules. To convert to microcalories, divide values by 4.184. To convert to mW m divide values by 10. 

Joule-Thompson Coefficient for Real Gases. This expresses the change in temperature with respect to change in pressure at constant enthalpy ... 

Tables 2,3, and 4 outline many of the physical and thermodynamic properties ofpara- and normal hydrogen in the sohd, hquid, and gaseous states, respectively. Extensive tabulations of all the thermodynamic and transport properties hsted in these tables from the triple point to 3000 K and at 0.01—100 MPa (1—14,500 psi) are available (5,39). Additional properties, including accommodation coefficients, thermal diffusivity, virial coefficients, index of refraction, Joule-Thorns on coefficients, Prandti numbers, vapor pressures, infrared absorption, and heat transfer and thermal transpiration parameters are also available (5,40). Thermodynamic properties for hydrogen at 300—20,000 K and 10 Pa to 10.4 MPa (lO " -103 atm) (41) and transport properties at 1,000—30,000 K and 0.1—3.0 MPa (1—30 atm) (42) have been compiled. Enthalpy—entropy tabulations for hydrogen over the range 3—100,000 K and 0.001—101.3 MPa (0.01—1000 atm) have been made (43). Many physical properties for the other isotopes of hydrogen (deuterium and tritium) have also been compiled (44).

Expansion from high to low pressures at room temperature cools most gases. Hydrogen is an exception in that it heats upon expansion at room temperature. Only below the inversion temperature, which is a function of pressure, does hydrogen cool upon expansion. Values of the Joule-Thorns on expansion coefficients for hydrogen have been tabulated up to 253 MPa (36,700 psi) (48), and the Joule-Thorns on inversion curve for i7n -hydrogen has been determined (49,50). 

The primary thermoelectric phenomena considered in practical devices are the reversible Seebeck, Peltier, and, to a lesser extent, Thomson effects, and the irreversible Eourier conduction and Joule heating. The Seebeck effect causes a voltage to appear between the ends of a conductor in a temperature gradient. The Seebeck coefficient, L, is given by... 

A more recent compilation includes tables giving temperature and PV as a function of entropies from 0.573 to 0.973 (2ero entropy at 0°C, 101 kPa (1 atm) and pressures from 5 to 140 MPa (50—1400 atm) (15). Joule-Thorns on coefficients, heat capacity differences (C —C ), and isochoric heat capacities (C) are given for temperatures from 373 to 1273 K at pressures from 5 to 140 MPa. 

To convert the Joule-Thomson coefficient, I, in degrees Celsius per atmosphere to degrees Fahrenheit per atmosphere, multiply by 1.8. 

TABLE 2-149 Additional References Available for the Joule-Thomson Coefficient... 

These derivatives are of importance for reversible, adiabatic processes (such as in an ideal turbine or compressor), since then the entropy is constant. An example is the Joule-Tnomson coefficient. 

FIG. 5-7 Radiation coefficients of heat transfer h,.. To convert British thermal units per hoiir-sqiiare foot-degrees Fahrenheit to joules per square meter-second-kelvins, multiply by 5,6783 = ( F — 32)/l,8,... 

Physical characteristics Molecular weight Vapour density Specific gravity Melting point Boiling point Solubility/miscibility with water Viscosity Particle size size distribution Eoaming/emulsification characteristics Critical temperature/pressure Expansion coefficient Surface tension Joule-Thompson effect Caking properties... 

For a compressible fluid that undergoes exansion through a valve or an orifice, the Joule-Thompson coefficient is defined as ... 

U = Heat transfer coefficient for transfer between the pipeline and surrounding ground, Btu/hr-ft -°F X = Distance from origin, ft Z = Distance above datum, ft = Joule-Thompson coefficient 6 = Incremental amount of a variable... 

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