Heat Capacities of Liquid Metals Above 1500 K
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HEAT CAPACITIES OF LIQUID METALS ABOVE 1500 K
JOHN L. MARGRAVE Department of Chemistry,
Rice University, Houston,
Texas
77001
Experimental heat capacity measurements for liquid metals by both the levitation and exploding wire techniques have shown that Cp values in the range 2000 - 5000 K may approach 10R for some metals and thus, significantly enhance the importance of liquid metals and heat sinks during nuclear excursions, 1 2 laser irradiations or high current pulses. ' The excess heat capacities can be related to other thermophysical properties through the equation 2
Cp - Cv = Celectronic + a VTBT where Celectronic = yT; a = the thermal expansion coefficient; V = the molar volume; and BT = the bulk modulus. Cv Z 3R for all liquid metals at T > 1500 K.
C (T) = 3R + YT + a 2VVTBT and often can be described by a general equation Cpl = a + bT + cT
2
+ ...
experimental support for the suggestion by Hoch et al3 There seems to be little that Cp's for liquid metals fit an equation like Cp
= a + bT + cT-2
which describes a few low-melting metals over temperature ranges of a few hundred degrees. Unfortunately, there is a paucity of experimental data for a, V or BT at high temperatures for solids and only a few investigators have studied liquid metals. For example, there are Cartesian Diver density determinations for a 4 few liquid metals by Kirschenbaum, Cahill and Grosse. There are a few density measurements for liquid metals by suspended drop techniques;5 and a few photo6 graphic density determinations on levitated liquid metal drops. In most cases the measurements are within a few hundred degrees of the melting points. 2 Gathers, Shaner, et a1 have used the exploding wire technique supplemented by fast photographic observations and fast multicolor optical pyrometry to obtain values for liquid metal densities and for liquid metal expansion coefficients over the range 500 - 5000 K for V, Pt, Nb, Mo, Ta, Ir, W, Pb and U. There seem to be few experimental determinations of bulk moduli over ranges of temperatures, although one has the intuitive feeling that they 2 Again, the exploding wire studies should decrease at temperature increases. which yield equations of state as well as other thermodynamic properties offer a unique source of experimental values for BT and for XT in the 2000 - 7000 K range. The electronic contributions to Cp are expected to be given by yT where y7 is the well-known coefficient derivable from low-temperature Cp-measurements. yT-contributions at low temperatures may be enhanced by electron-phonon interactions but this should not be important in high temperature liquids. Typical values for y from low temperature studies are in the range 10-3 to 10-4 cal 2 mol-I K7 . By collecting these ideas and utilizing both levitation and exploding wire data for liquid metals, one can estimate the Cp-values listed in Table I.
40 Since Cp (5000) falls in the range BR to 10R for many liquid metals, one can more confidently assign heat loads and predict structure survival during extreme temperature
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