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1.          Background Theory

Table B1. Thermal emf in absolute mV for T-Type thermocouple with ref. =0°C. [Holman]

Temperature (°C)	Voltage (mV)
-184.4	-5.341
-156.7	-4.745
-128.9	-4.419
-101.1	-3.365
-73.3	-2.581
-45.55	-1.626
-17.8	-0.674
10	0.422
37.8	1.518
65.6	2.743
93.3	3.967
121.1	5.307

 

Figure B1. Temperature plot as a funcion of voltage displayed.

 

From Figure B1., we obtain the calibrition equation:

 

                                                                       [Eqn. 1]

 

T: Temperature measured.

V: Voltage displayed

When a temperature measurement is not made under steady-state conditions, the energy balance for the changing thermal system may be written as:

 

                                                                     [Eqn. 3]

 

.h: Convection heating transfer coefficient between the thermometer and the fluid.

A: Surface area of the thermal system.

: Temperature of the environment.

T: Temperature measured.

 

Eqn. 3 may also be written as the temperature of the thermometer as a function of time:

 

                                                                 [Eqn. 4]

 

: Temperature of the thermometer at time zero.

Other variables are defines as in above.

 

Eqn. 4 is often rewritten as:

                                                                        [Eqn. 5]

 in which , the time constant, is defined as mc/hA

 

It is possible to linearize Eqn. 5 into the following form:

 

   =                         [Eqn. 6]

If Eqn. 6 is plot as a function of time, the slope will be equal to , the time constant can thus be calculated from known temperature at different time intervals.