The 1962 He3 scale of temperatures. II. Derivation

Abstract

An Experimental Thermodynamic Equation (ETE) temperature scale valid from 0.2 to 2.0 °K has been calculated for He³. The scale is based on new comparisons, (<i>P</i> ₃, <i>P</i> ₄),of He³ and He⁴ vapor pressures above 0.9 °K; on the 1958 He⁴ temperature scale; and on the best available data for several thermodynamic properties of He³ from 0.2 to 2.0 °K. The <i>T</i> ₆₂ Full-Range Working Equation (FWE) scale, <DispFormula> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>ln</mml:mi> <mml:msub><mml:mi>P</mml:mi> <mml:mn>3</mml:mn></mml:msub> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mn>2.49174</mml:mn> <mml:mo>/</mml:mo> <mml:mi>T</mml:mi> <mml:mo>+</mml:mo> <mml:mn>4.80386</mml:mn> <mml:mo>-</mml:mo> <mml:mn>0.286001</mml:mn> <mml:mtext> </mml:mtext> <mml:mi>T</mml:mi> <mml:mo>+</mml:mo> <mml:mn>0.198608</mml:mn> <mml:mtext> </mml:mtext> <mml:msup><mml:mi>T</mml:mi> <mml:mn>2</mml:mn></mml:msup> <mml:mo>-</mml:mo> <mml:mn>0.0502237</mml:mn> <mml:mtext> </mml:mtext> <mml:msup><mml:mi>T</mml:mi> <mml:mn>3</mml:mn></mml:msup> <mml:mo>+</mml:mo> <mml:mn>0.00505486</mml:mn> <mml:mtext> </mml:mtext> <mml:msup><mml:mi>T</mml:mi> <mml:mn>4</mml:mn></mml:msup> <mml:mtext> </mml:mtext> <mml:mo>+</mml:mo> <mml:mn>2.24846</mml:mn> <mml:mtext> ln </mml:mtext> <mml:mi>T</mml:mi></mml:mrow> </mml:math> </DispFormula> fits the ETE scale and the (<i>P</i> ₃, <i>T</i> ₅₈) data and is therefore valid for use from 0.2 to the critical point, 3.324 °K. The maximum deviation from the ETE scale is 0.4 mdeg and the standard deviation from the input data is 0.25 mdeg. The fit to the seven recalculated isotherms of Keller in the range of the 1962 He³ scale can be determined by converting Keller's <i>P</i> ₄'s to equivalent <i>P</i> ₃'s, using direct <i>P</i> ₄ to <i>P</i> ₃ interpolation equations. The fit of the 1962 He³ scale is as good as the fit of the 1958 He⁴ scale to the same isotherms, the average displacements of the two scales both being 1.5 mdeg below the isotherms. The average standard deviations for (<i>T</i> ₆₂-<i>T</i> _iso) and for (<i>T</i> ₅₈-<i>T</i> _iso) are 1.2 and 1.0 mdeg, respectively, for these seven isotherms.