Dynamic Response of Temperature Measuring Devices
(Transient Heat Transfer)
This experiment has two main goals. First, to introduce the basic operating principles of
several common methods of temperature measurement such as, liquid-in-glass thermometers,
thermocouples and thermistors and how to calibrate these devices. Second, to introduce the
concept of dynamic response of thermal systems, ways of measuring this response and factors,
which influence this behavior.
Temperature Measuring Devices
When a pair of electrical conductors (metals) are joined together, a thermal emf is generated
when the junctions are at different temperatures. This phenomenon is known as the Seebeck effect.
Such a device is called a thermocouple. The resultant emf developed by the thermocouple is in the
millivolt range when the temperature difference between the junctions is 100 0C. To determine
Figure 1 - Measuring the EMF of a Thermocouple
the emf of a thermocouple as a function of the temperature, one junction is maintained at some
constant reference temperature, such as ice-water mixture at a temperature of 0 0C. The thermal
emf, which can be measured by a digital voltmeter as shown in Figure 1, is proportional to the
temperature difference between the two junctions. To calibrate such thermocouple the temperature
of the second junction can be varied using a constant temperature bath and the emf recorded as a
function of the temperature difference between the two nodes.
The output voltage, E, of such a simple thermocouple circuit is usually written in the form,
E AT BT 2 CT 3 (1)
where T is the temperature in 0C, and E is based on a reference junction temperature of 0 0C. The
constants A, B and C are dependent on the thermocouple material.
Providing a fixed reference temperature for the reference junction using an ice bath can
make the use of a thermocouple cumbersome. Hence, commercially available thermocouples
usually consist of two leads terminating in a single junction. The leads are connected to a
thermocouple signal conditioning „box‟ containing an electrical circuit which provides a reference
voltage equal to that produce by a reference junction placed at 0 0C, a process called „ice point
compensation‟. These thermocouple signal conditioners or „power supplies‟ usually display the
temperature directly and or provide a voltage output that is proportional to the thermocouple
temperature. A similar thermocouple signal conditioner with a digital temperature display and an
analog voltage output is used in the present experiment.
The thermistor, a thermally sensitive resistor, is a solid semiconducting material. Unlike
metals, thermistors respond inversely to temperature, i.e., their resistance decreases as the
temperature increases. The thermistors are usually composed of oxides of manganese, nickel,
cobalt, copper and several other nonmetals. The resistance is generally an exponential function of
the temperature, as shown in Equation 2:
R 1 1
R T T (2)
where R0 is the resistance at a reference temperature, T0, while is a constant, characteristic of the
material. T0, the reference temperature, is generally taken as 298 K (25 0C). Since all
measurements made with thermistors can be reduced to detecting the resistance changes, the
thermistor must be placed in a circuit and the resistance changes recorded in terms of the
corresponding voltage or current changes. The formula relating the voltage (or current) changes to
the resistance changes for a given circuit has to be determined theoretically or empirically, or by a
combination of both.
In the design of thermistor circuits, one must take the precaution that within the range of the
operating conditions; the circuit remains stable at all times. Thermistor resistance varies inversely
with temperature. The voltage applied directly across a thermistor causes its temperature to rise,
and its resistance to decrease. Sufficiently high voltage may cause thermal "runaway" (curve A in
Figure 2), in which condition, higher currents and temperatures are induced until the thermistor
Figure 2 - Thermistor Behavior and Thermal Runaway
fails, or the power is reduced. A series resistor, introduced to limit current, ensures stability (curve
B). Thermal "runaway" will, in all probability, permanently damage the thermistor, or change its
To increase the precision of the measurement, one should add a voltage divider to the circuit
shown in Figure 3(a). This will convert it to a Wheatstone bridge circuit, as shown in Figure 3(b).
The out-of-balance voltage, V, can then be measured and related to the resistance of the
thermistor. A correct choice of resistors R2 and R3 will remove the mean DC value of V. Note
that although the bridge circuit can increase the precision of the readings, the sensitivity is still the
same as for the simple voltage divider circuit shown in Figure 3(a). The simple DC bridge circuit
of Figure 3(b) is generally satisfactory for most applications.
Figure 3 - Thermistor Circuit
Considering this circuit, we now derive the relation between T and V. In general,
V E R R R R (3)
2 3 1 T
Assume R1 = R3. Then,
V E R R R R (4)
1 2 1 T
Rearranging for RT,
ER V R1 R2
ER V R R
RT R1 2 (5)
1 1 2
The relation between T and RT is given by,
RT R0 exp
T T (6)
1 1 1 R
ln T (7)
T T0 R0
Substituting for RT from Equation 5, we have
1 1 1 R1 ER2 V R1 R2
T T0 R0 ER1 V R1 R2
If we further assume R1 = R2 = R3 = Rb, we have,
1 1 1 R E 2V
ln b (9)
T T0 R0 E 2V
T is not a linear function of V, and so any linear analog recorder will be in error when linear
interpolation is used between calibration points (for small ranges in temperatures, the error may be
negligible). If we measure E along with our scans of the Vs, then the only unknowns in Equation
9 are R0 and . These unknowns are determined by static calibration experiment. You will perform
a 3 or 4 point static calibration of both the thermocouple and the thermistor.
Dynamic Response of Thermal Systems
When temperature measurements of a transient process are made, it is important to verify
that the dynamic response of the measuring device is fast enough to accurately track the time
varying temperature. In the second part of this experiment, we will study the influence of different
parameters on the transient response characteristics of a thermal system. In this experiment, we will
measure the response of thermocouple (or a modified thermocouple). The thermocouple is modeled
as a spherical ball, as shown in Figure 4. The thermocouple temperature is, T, mass m and specific
Figure 4 – Thermocouple bead modeled as a simple thermal system
heat capacity c. If the sphere is suddenly exposed to an environment at temperature T, then, after
making the appropriate assumptions, the energy balance for this transient process is given by:
hA(T T ) mc
The solution for the above first order equation is the well known exponential decay given as:
e ( ha / mc)
where the time constant = mc/hA. In this experiment, we will examine the influence of properties
suh as mass, surface area and specific heat capacity of the bead on its dynamic response.
The following apparatus is used in conducting the experiments:
1. Constant temperature bath: The constant temperature bath is capable of providing
liquids at constant temperatures between approximately 10 to 90 0C. Several different
temperatures will be used in the calibration procedure. Note how the settings are made
and set the bath for a low temperature.
2. Thermocouples: The thermocouple used in this experiment is connected to a power
supply, which has a digital temperature display and an analog output. The analog output
is connected to the ADC card. The thermocouple will be calibrated by placing it in the
constant temperature bath and recording the digital display and the voltage output using
the computer and the ADC card.
3. Thermistor: Examine the thermistor provided; it will already be connected to a
Wheatstone bridge circuit. You will calibrate it by placing it in the constant temperature
bath along with the thermocouple and recording the output voltage. Thermocouples
with different beads.
4. Wheatstone bridge circuit: For the thermistor.
5. Personal Computer and Analog-to-Digital (ADC) converter: This will be used to
digitize and record the voltage signal form the thermocouple and thermistor as a
function of time.
6. Resistance Temperature Detector (RTD): The RTD will be immersed in the constant
temperature bath for the duration of the experiment. The temperature indicated by the
RTD will serve as the reference temperature (i.e., actual temperature of the bath).
Pictures of the hardware can be found here (insert a link to pictures of the hardware).
I. Thermocouple and Thermistor Static Calibration
The static calibration for the thermocouple and the thermistor will be done at the same time.
1. Connect the outputs of the thermocouples and the thermistor to the appropriate channels
on the ADC card. Start the LabView program that is used for data acquisition. Ask the
TA‟s for assistance.
2. Place the thermocouple and the thermistor in the constant temperature bath. Place the in
the constant temperature bath. Starting with the bath at the lowest setting, between 20 –
3. Record the temperature of the RTD.
4. Record the thermocouple temperature and the voltage reading.
5. Record the thermistor out-of-balance voltage, V, and
6. Repeat for three other different temperatures.
II. Time Response Measurement
1. Set the constant temperature bath between 20 and 40 0C.
2. Using the LabView program provided, monitor and record the outputs of the
thermocouple as you rapidly move the thermocouple from the constant temperature bath
and place them in the ice bath.
3. Now change the constant temperature bath temperature to somewhere between 60 and
80 0C and repeat step 2.
4. Without changing the constant bath temperature, repeat step 2 with the larger size
“thermocouples”. Note the diameter and the material of all the thermocouple beads.
Questions to be answered
1. Discuss the principles of operation of thermocouples and thermistors. Compare the
advantages and drawbacks of using the two devices.
2. Plot the static calibration data for the thermocouple and the thermistor, i.e. plot
temperature vs. voltage. Does the voltage output confirm the expected trends? How and
3. Is the temperature in the constant temperature bath truly constant? Did you notice
temperature fluctuations, and if so, what was their magnitude? What is the effect of
these fluctuations on the accuracy of your static calibration?
4. Is there a discrepancy in the RTD temperature and the temperature displayed on the
thermocouple digital display? Is the discrepancy constant over the entire temperature
range? Discuss reasons for this discrepancy.
5. Determine the time constants for the smallest thermocouple at the two different
temperature settings. Would you expect the time responses to be the same or different
6. Determine and compare the time constants for the larger diameter thermocouples.
Keeping in mind the physical parameters which govern the time response, is this trend