1 



100 



/ R 100 ^ 



Ki - 



\ioo / 



T \ 



s 



100 



(2) 



(3) 



S ) 



where T is temperature in °C, R^ and R are resis- 

 tances at T°C and 0°C respectively, Rioo and R s 

 are resistances at 100° and melting point of 

 sulfur respectively and T s is temperature of 

 melting point of sulfur. Representative values 



for a. and S are 0.00392 and 1.^9, respectively, 



„-o 



giving a nonlinearity over 

 mately 0.1$. 



25° span of approxi- 



In order to obtain a reasonably dimensioned 

 package, together with rapid thermal response, a 

 small diameter tube was utilized for the element 

 housing. This combines a relatively low mass 

 with a short thermal path and high structural 

 strength. In practice, a flexible mandrel is 

 wound spirally with reference grade platinum 

 resistance wire. Over this spiral, aluminum 

 oxide or beryllium oxide beads are threaded, 

 leads affixed, the whole slipped into a tube and 

 the assembly then swaged down to final form. 

 Total tube diameter approximates 0.060 inch and 

 in one configuration the outer tube wall is 

 0.006 inch thick. 



TIME CONSTANT 



The thermal response of a probe can be calcu- 

 lated as the algebraic sum of the separate time 

 constants. The thermal situation is analogous 

 to an electrical network of resistance and capaci- 

 tance where the time constant, T, is equal to 

 RC (Fig. 2). For a cylinder of unit length, 



In =- 

 r l 



R = 



2ttK 



C = TTPCt: 



*2 2 -*L 2 



RC 



pC p 

 W 



(» $(* - *■). 



00 



(5) 



(6) 



(0) THERMAL 



CONFIGURATION 



(b) ELECTRICAL 

 EQUIVALENT 



Fig. 2. Schematic diagram of (a) thermal con- 

 figuration and (b) electrical equivalent 

 for calculation of thermal response. 



Table I. Thermal probe constants. 



Parameter 



^2 is outside radius of 

 cylinder in feet 



r^ is inside radius of 

 cylinder in feet 



p is density #/ft3 



C p is specific heat Btu/#/°F 



K is conductivity 

 Btu/hr/ft/°F 



Stainless Aluminum 

 Steel Oxide 



0.00233 0.00175 



0.00175 0.00092 

 i+98. 230. 

 0.175 0.125 



9-5 



1.0 



In the probe, which consists essentially of a 

 metal cylinder surrounding a ceramic cylinder 

 with the element beneath, the time constant of 

 the sheath equals 



rc ( 0+98) (0.125) )( / l n Q- 00233 ) fo.00233 2 

 V (9-5) (2) /V 0.00175 7 V 



0.00175' 







The values of constants in the above equations 

 for the particular probe under consideration are 

 given in Table I. 



= 0.322 x 10 _ 5 hrs 

 = 0.0166 sec 



kk 



