process instrumentation i module code: eipin1b study ... - Home Mweb

EIPINI Chapter 5: Temperature Measurement Page 5-22
Example 5-14
The following equations are provided for a type K thermocouple, to calculate
temperature (t in °C) from emf (v in μV) in the temperature range 0 °C to 500 °C:
t = (2.508355×10 -2 )v + (7.860106×10 -8 )v 2 - (2.503131×10 -10 )v 3
+ (8.315270×10 -14 )v 4 – (1.228034×10 -17 )v 5 + (9.804036×10 -22 )v 6
- (4.413030×10 -26 )v 7 + (1.057734×10 -30 )v 8 – (1.052755×10 -35 )v 9 ,
Equation (a)
and to calculate emf (v in μV) from temperature (t in °C) in the temperature range
0 °C to 1372 °C:
v = -17.600413686 + 38.921204975t + (1.8558770032×10 -2 )t 2
- (9.9457592874×10 -5 )t 3 + (3.1840945719×10 -7 )t 4
- (5.6072844889×10 -10 )t 5 + (5.6075059059×10 -13 )t 6
- (3.2020720003×10 -16 )t 7 + (9.7151147152×10 -20 )t 8
− 4
2
– (1.2104721275×10 -23 )t 9 + 118.5976e
−1.183432×
10 (t −126.9686)
Equation (b)
a) Use Equation (a) to calculate the temperature when the emf is 2602 μV.
b) Use Equation (b) to calculate the emf when the temperature is 20 °C.
a) t = (2.508355×10 -2 )×2602 + (7.860106×10 -8 )×2602 2 - (2.503131×10 -10 )×2602 3
+ (8.315270×10 -14 )×2602 4 – (1.228034×10 -17 )×2602 5 + (9.804036×10 -22 )×2602 6
- (4.413030×10 -26 )×2602 7 + (1.057734×10 -30 )×2602 8 – (1.052755×10 -35 )×2602 9
= 65.26740 + 0.5321609 – 4.409664 + 3.811584 – 1.464694 + 0.3042627
- 0.03563592 + 0.002222464 – 0.05755631
= 63.95 °C
b) v = -17.600413686 + 38.921204975×20 + (1.8558770032×10 -2 )×20 2
- (9.9457592874×10 -5 )×20 3 + (3.1840945719×10 -7 )×20 4
- (5.6072844889×10 -10 )×20 5 + (5.6075059059×10 -13 )×20 6
- (3.2020720003×10 -16 )×20 7 + (9.7151147152×10 -20 )×20 8
− 4
2
– (1.2104721275×10 -23 )×20 9 + 118.5976e
−1.183432×
10 (20 −126.9686)
= -17.600414 + 778.4241 + 7.423508 – 0.7956607 + 0.05094551
- 0.001794331 + 35.88804×10 -6 – 409.8652×10 -9 + 2.487069×10 -9
- 6.197617×10 -12 + 30.61899
= 798.1 microvolt
(Compare these answers to those of Example 5-11)
5.10.6 Compensating leads
Thermocouple thermometers are normally installed some distance away from the
voltmeter or computer that measures the emf generated by the thermocouple. For
this purpose, cheaper and lower grade thermocouple wires, called extension wire or
compensating leads, are used to connect the thermocouple to the measuring device
at the reference junction. Compensating leads have the same thermoelectric