Vol. 60
1344
COMMUNICATIONS TO THE EDITOR EXTRAPOLATION OF COOLING CURVES IN MEASUREMENTS OF HE.4T CAPACITY Sir:
pure. A new batch has been prepared, and the results of the measurements will be reported later. The present treatment of cooling curves is an extension of the method proposed by Barieau and Giauque.2 TABLE I
During measurement of the heat of fusion of phosphoric acid hemihydrate, 2H3POa.Hz0(m.p. 29.32”’) in an adiabatic calorimeter, a fairly comEXTRAPOLATION OF COOLING CURVES mon situation arose in which the approach to Time after Temperature,O I(. heat 08, min. Point 118 Point 119 Point 120 temperature equilibrium was so slow as to require analytical or graphical estimation of the equilibrium 14 302.3258 302.6133 temperature. The method of treatment cited most 24 302.3264 often seems t o be one reported by Barieau and 92 302.3118 Giauque.2 The data for three such points are 95 302.3080 treated here by three methods. 219 302.3086 In method 112values of -In (dT/dt), where T t = m represents temperature and t time, were plotted Method 1 302.3038 302.2967 302.3016 against time, and a linear equation was fitted to the Method 2 302.3012 302.3030 302.2973 data Method 3 302.3038 302.3032 302.2982 -In (dT/dt) = A - Bt DIVISION OF CHEMICAL DEVELOPMENT This equation was integrated to give TENNESSEE VALLEY AUTHORITY EDWARD P. EGAN, JR. WILSONDAM,ALABAMA InB(Tt - T,) = A - Bt RECEIVED JULY2, 1956 and the value of the integral was added to a value of T at a selected time, t . In method 2, the cooling curve was taken as a SECOND EXPLOSION LIMITS OF CARBON MONOXIDE-OXYGEN MIXTURES section of a hyperbola of the form T = TI, - ( t - r!k)/(A + Bt) Sir: In our recent criticism’ of a paper by von Elbe, where Tk and lk represent temperature at a selected time. The equation was solved for large values of Lewis and Roth12one of our points concerned the 1, to extend the equation to the asymptote, and the derivation of their equation 2. In our derivation of value of T so obtained was taken as the equilibrium the explosion condition, we neglected to consider their reaction temperature. In method 3, T was plotted against l / t and a co + 0s +con + 20 (111) straight line was drawn through the points to inter- We wish to point out that when equation (111) is cept the Taxis at t = =, included, their equation 2, in which k3 does not Table I shows the results for the first and last explicitly appear, is correctly derived. measured points in each series. The values of T at DIVISION ALVINS. GORDON infinite time are in good agreement for such a long CHEMISTRY U. S. NAVALORDNANCE TESTSTATION R. H. KNIPE extrapolation. CHINALAKE,CALIFORNIA The particular preparation of phosphoric acid RECEIVED AUGUST10, 1956 hemihydrate for which part of the measurements (1) A. S. Gordon and R . H. Knipe.Tals JOURNAL. 60, 1023 (1956). are reported here was found to be not sufficiently (2) G. von Elbe, B. Lewis and W. Roth, “Fifth Symposium on (1) W. H. Roes and R.M.Jones, TRIBJOURNAL, 47, 2165 (1925) . F. Giauque, i6id., 72, 5676 (1950). (2) R. E. Barieau and W
Combustion,” Reinhold Publishing Co., New York, N. Y., 1955, p. 010.
