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熱電対の起電力の式

以下に、JIS C1602 に記述されている起電力表を多項式で表した式を示す。 温度が であり、$E_{mf}$$\mu$V で示される。

Type B:

Emf (t) = - 2.467460162 x 10-1t + 5.9102111169 x 10-3t2 - 1.430712343 x 10-6t3  
    + 2.150914975 x 10-9t4 - 3.175780072 x 10-12t5 + 2.4010367459 x 10-15t6  
    - 9.0928148159 x 10-19t7 + 1.3299505137 x 10-22t8  
    (0℃ < t <1820℃) (3.3)

Type E:

Emf (t) = 5.86958578 x 10t +5.1667517705 x 10-2t2 -4.4652683347 x 10-4t3  
    -1.7346270905 x 10-5t4 -4.8719368427 x 10-7t5 -8.8896550447 x 10-9t6  
    -1.0930767375 x 10-10t7 -9.1784535039 x 10-13t8 -5.2575158521 x 10-15t9  
    -2.0169601996 x 10-17t10 -4.9502138782 x 10-20t11 -7.0177980633 x 10-23t12  
    -4.3671808488 x 10-26t13 (-270℃ < t < 0℃)  
  = 5.8695857799 x 10{+01}t +4.3110945462 x 10-2t2 +5.7220358202 x 10-5t3  
    -5.4020668085 x 10-7t4 +1.5425922111 x 10-9t5 -2.4850089136 x 10-12t6  
    +2.3389721459 x 10-15t7 -1.1946296815 x 10-18t8 +2.5561127497 x 10-22t9  
    (0℃ < t < 1000℃) (3.4)

Type J:

Emf (t) = 5.0372753027 x 10+01t +3.0425491284 x 10-2t2 -8.5669750464 x 10-5t3  
    +1.3348825735 x 10-7t4 -1.7022405966 x 10-10t5 +1.9416091001 x 10-13t6  
    -9.6391844859 x 10-17t7 (-270℃ < t < 760℃)  
  = 2.9721751778 x 10+05t -1.5059632873 x 10+03t2 +3.2051064215 x 10+00t3  
    -3.2210174423 x 10-3t4 +1.5949968788 x 10-6t5 -3.1239801752 x 10-10t6  
    (760℃ < t < 1200℃) (3.5)

Type K:

Emf (t) = -18.533063273 +38.918344612 t +1.6645154356 x 10-2t2  
    -7.8702374448 x 10-5t3 +2.2835785557 x 10-7t4 -3.5700231258 x 10-10t5  
    +2.9932909136 x 10-13t6 -1.2849848798 x 10-16t7 +2.2239974336 x 10-20t8  
    +125 exp[-0.5(t-127.0/65)2] (0℃ < t < 1372℃) (3.6)

Type R:

Emf (t) = 5.289139 t +1.391111 x 10-2t2 -2.400524 x 10-5t3 +3.620141 x 10-8t4  
    -4.464502 x 10-11t5 +3.849769 x 10-14t6 -1.537264 x 10-17t7  
    (-50℃ < t < 630.74℃)  
  = -264.1801 +8.046868t +2.989229 x 10-3t2 -2.687606 x 10-7t3  
    (630.74℃ < t < 1064.43℃)  
  = 15540.414 +4235.7773((t-1365)/300) +14.69308((t-1365)/300)2 -52.213890((t-1365)/300)3  
    (1064.43℃ <t < 1665.0℃)  
  = +2.0416695 x 10+4 +6.6850914 x 10+2(t-1715)/50 -12.301472((t-1715)/50)2  
    -2.7861521((t-1715)/50)3 (1665℃ < t < 1767.6℃) (3.7)

Type S:

Emf (t) = 5.399578 x 10 t +1.251997 x 10-2t2 -2.244822 x 10-5t3 +2.845216 x 10-8t4  
    -2.244058 x 10-11t5 +8.505417 x 10-15t6 (-50℃ < t < 630.74℃)  
  = -2.982448 x 102 +8.237553 t +1.645391 x 10-3t2 (630.74℃ < t < 1064.43℃)  
  = 13943.448 +3637.56722177\frac{t-1365}{300} +1.41575957(\frac{t-1365}{300})2  
    -45.9074898(\frac{t-1365}{300})3 (1064.43℃ <t < 1665.0℃)  
  = 18113.083 +567.95375\frac{t-1715}{50} -12.112492(\frac{t-1715}{50})2 -2.8117589(\frac{t-1715}{50})3  
    (1665℃ < t < 1767.6℃) (3.8)

Type T:

Emf (t) = 38.740773840 t +4.4123932482 x 10-2t2 +1.1405238498 x 10-4t3 +1.9974406568 x 10-5t4  
    +9.0445401187 x 10-7t5 +2.2766018504 x 10-8t6 +3.6247409380 x 10-10t7  
    +3.8648924201 x 10-12t8 +2.8298678519 x 10-14t9 +1.4281383349 x 10-16t10  
    +4.8833254364 x 10-19t11 +1.0803474683 x 10-21t12 +1.3949291026 x 10-24t13  
    +7.9795893156 x 10-28t14 (-270℃ < t < 0℃)  
  = 38.740773840 t +3.3190198092 x 10-2t2 +2.0714183645 x 10-4t3 -2.1945834823 x 10-6t4  
    +1.1031900550 x 10-8t5 -3.0927581898 x 10-11t6 +4.5653337165 x 10-14t7  
    -2.7616878040 x 10-17t8 (0℃ < t < 400℃) (3.9)

Type N:

Emf (t)= 26.159105962 t +1.0957484228 x 10-2t2 -9.3841111554 x 10-5t3 -4.6412039759 x 10-8t4  
  -2.6303357716 x 10-9t5 -2.2653438003 x 10-11t6 -7.6089300791 x 10-14t7  
  -9.3419667835 x 10-17t8 (-270℃ < t < 0℃)  
  25.929394601 t +1.5710141880 x 10-2t2 +4.3825627237 x 10-5t3 -2.5261169794 x 10-7t4  
  +6.4311819339 x 10-10t5 -1.0063471519 x 10-12t6 +9.9745338992 x 10-16t7  
  -6.0863245607 x 10-19t8 2.0849229339 x 10-22t9 -3.0682196151 x 10-26t10  
  (0℃ < t < 1300℃) (3.10)

以上の多項式の計算に用いられる関数を,C言語で記述すれば次のようになる。 polyfunc は多項式の計算であり,revfunction は逆関数で,起電 力から温度を求める時に用いる。

/* ---------------------------------------------------------- *
 * 多項式の計算
 */
double
polyfunc (int cn, double c[], double d)

    int    i;
    double x, s;
    
    x = 1.0;
    s = 0;
    for (i = 0; i < cn; i++) {
        s += c[i] * x;
        x *= d;
    
    return s;
}
/* 逆関数の計算 */
int iter = 0;          /* number of iteration */

double
revfunction(double einit, double e, double(*funct)(double)) 
{
    double y1, t1, t2, t;
    
    t1 = einit;
    y1 = funct(t1);
    t2 = t1 + DELTA_T;
    iter = 0;
    while (iter < 20) {
        double dy, y2, err;
        y2 = funct(t2);
        dy = y2 - y1;
        err = fabs(dy);
        if (err < EPSILON)
            break;
        t = t2 - (y2 - e) * (t2 - t1) / (y2 - y1);
        y1 = y2;
        t1 = t2;
        t2 = t;
        iter++;
    }
    return t;
}


next up previous contents index
Next: 抵抗測温体 Up: 熱電対(サーモカップル)と熱電堆(サーモパイル) Previous: サーモパイル   目次   索引
Ken Kishimoto 2014-06-02