E1C08 09/14/2010
14:54:1 Page 344
ASSUMPTION Thermocouple follows NIST standard emf behavior.
FIND The temperature of the measuring junction.
SOLUTION By the law of intermediate temperatures the output emf for a thermocouple circuit
having two junctions, one at 0
C and the other at T 1 , would be the sum of the emfs for a
thermocouple circuit between 0
and 30
C and between 30
C and T 1 . Thus,
emf 0À30 þ emf 30ÀT 1 ¼ emf 0ÀT 1
This relationship allows the voltage reading from the nonstandard reference temperature to be
converted to a 0
C reference temperature by adding emf 0À30 ¼ 1:537 to the existing reading. This
results in an equivalent output voltage, referenced to 0
C as
1:537 þ 8:132 ¼ 9:669 mV
Clearly, this thermocouple is sensing the same temperature as in the previous example, 180.0
C.
This value is determined from Table 8.6.
COMMENT Note that the effect of raising the reference junction temperature is to lower the output
voltage of the thermocouple circuit. Negative values of voltage, as compared with the polarity listed in
Table 8.4, indicate that the measured temperature is less than the reference junction temperature.
Example 8.9
A J-type thermocouple measures a temperature of 100
C and is referenced to 0
C. The thermocouple is AWG 30 (American wire gauge [AWG]; AWG 30 is 0.010-in. wire diameter) and is
arranged in a circuit as shown in Figure 8.17a. The length of the thermocouple wire is 10 ft in order
to run from the measurement point to the ice bath and to a potentiometer. The resolution of the
potentiometer is 0.005 mV. If the thermocouple wire has a resistance per unit length, as specified by
the manufacturer, of 5:6 V=ft, estimate the residual current in the thermocouple when the circuit is
balanced within the resolution of the potentiometer.
KNOWN A potentiometer having a resolution of 0.005 mV is used to measure the emf of a Jtype thermocouple that is 10 ft long.
FIND The residual current in the thermocouple circuit.
SOLUTION The total resistance of the thermocouple circuit is 56 V for 10 ft of thermocouple
wire. The residual current is then found from Ohm’s law as
I ¼
E
R
¼
0:005 mV
56 V
¼ 8:9 Â 10
À8 A
COMMENT The loading error due to this current flow is $ 0:005 mV=54:3 mV=
C % 0:09
C.
Example 8.10
Suppose a high-impedance voltmeter is used in place of the potentiometer in Example 8.9.
Determine the minimum input impedance required for the voltmeter that will limit the loading
error to the same level as the potentiometer.
344 Chapter 8 Temperature Measurements
14:54:1 Page 344
ASSUMPTION Thermocouple follows NIST standard emf behavior.
FIND The temperature of the measuring junction.
SOLUTION By the law of intermediate temperatures the output emf for a thermocouple circuit
having two junctions, one at 0
C and the other at T 1 , would be the sum of the emfs for a
thermocouple circuit between 0
and 30
C and between 30
C and T 1 . Thus,
emf 0À30 þ emf 30ÀT 1 ¼ emf 0ÀT 1
This relationship allows the voltage reading from the nonstandard reference temperature to be
converted to a 0
C reference temperature by adding emf 0À30 ¼ 1:537 to the existing reading. This
results in an equivalent output voltage, referenced to 0
C as
1:537 þ 8:132 ¼ 9:669 mV
Clearly, this thermocouple is sensing the same temperature as in the previous example, 180.0
C.
This value is determined from Table 8.6.
COMMENT Note that the effect of raising the reference junction temperature is to lower the output
voltage of the thermocouple circuit. Negative values of voltage, as compared with the polarity listed in
Table 8.4, indicate that the measured temperature is less than the reference junction temperature.
Example 8.9
A J-type thermocouple measures a temperature of 100
C and is referenced to 0
C. The thermocouple is AWG 30 (American wire gauge [AWG]; AWG 30 is 0.010-in. wire diameter) and is
arranged in a circuit as shown in Figure 8.17a. The length of the thermocouple wire is 10 ft in order
to run from the measurement point to the ice bath and to a potentiometer. The resolution of the
potentiometer is 0.005 mV. If the thermocouple wire has a resistance per unit length, as specified by
the manufacturer, of 5:6 V=ft, estimate the residual current in the thermocouple when the circuit is
balanced within the resolution of the potentiometer.
KNOWN A potentiometer having a resolution of 0.005 mV is used to measure the emf of a Jtype thermocouple that is 10 ft long.
FIND The residual current in the thermocouple circuit.
SOLUTION The total resistance of the thermocouple circuit is 56 V for 10 ft of thermocouple
wire. The residual current is then found from Ohm’s law as
I ¼
E
R
¼
0:005 mV
56 V
¼ 8:9 Â 10
À8 A
COMMENT The loading error due to this current flow is $ 0:005 mV=54:3 mV=
C % 0:09
C.
Example 8.10
Suppose a high-impedance voltmeter is used in place of the potentiometer in Example 8.9.
Determine the minimum input impedance required for the voltmeter that will limit the loading
error to the same level as the potentiometer.
344 Chapter 8 Temperature Measurements