Subsurface Laboratory Methods 249 



Factor A defines the quantity of heat added to or subtracted from 



dH , 



the test specimen owing to reaction. In an exothermic reaction is posi- 



dt 



tive. Factor B ^^ defines the quantity of heat absorbed by the specimen ^^ 

 A + B =C, because at any point x along the differential-thermal curve, 

 the amount of heat used in raising the temperature of the specimen must 

 equal the amount brought in by flow from the metal block plus the 

 amount added or subtracted by the reaction. 



In the event sample factor a does not exist, the heat which flows in 

 B' must equal the heat used in raising the temperature of the specimen C. 

 Let C=C + AC 



and k'=k+ Ak 



Also in the experimental procedure Mo=Mo' within the error of 

 measurement. Subtracting (3) from (2) and rearranging gives: 



M r^dt+gk Civ-Ddt-gAK r{To-r)dt 



J adt J a J a 



=Mo\C[{T-Ta)-{r-Ta')]-AC[r-Ta']\ ^^^ 



=Mo\D[{T-r)-Ta-Ta')]-AC[T'-Ta']\ 



As T'— r=r=temperature indicated by the differential thermocouple, the 

 equation can be considerably simplified by assuming that the term con- 

 taining {To—T'), C, and K are small in comparison with other terms. By 

 using a and c as integration limits : 



M r^dt+g . k (\Tdt=MoC[ {T-Te') -{Ta-Tr!) 1 (5) 



J adt J a) 



but to a close approximation ^^ 



and 



J<^dH 

 ~dt=MAH, 



the total heat of reaction 



,o,ES^ = r\Tdt. (6) 



The last expression is proportional to the area enclosed by a straight 

 line from a to c and the curve ahc, if the deviation from the base line 

 is a linear function of the differential temperature. It is proportional, 

 therefore, to the percentage of reacting material in a given weight of 



°^ The temperature gradient in the chrome-nickel steel can be neglected as the thermal conductivity 

 of the metal is so much greater than that of the refractory sample to be tested. 



°' (Ta — Ta) and (Tc- -Tc) will equal zero for specimen holders in which the test and alundnm 

 holes are symmetrically spaced relative to the heat source. In the present concentric type of spacing 

 \Ta — Ta) = (Tc — Tc) within the error of measurement. 



