Comprehensive Analysis of Temperature Sensors: Sensitivity, Calibration, and Error Assessment in Temperature Measurement

OBJECTIVES

1. Calibration of different types of temperature sensors.
2. Measurement of temperature distribution along a rod
3. Measurement of surface temperature.

CALCULATIONS AND DISCUSSION

Tables and Graphs are attached behind this report.

a)

Sensitivity of the sensors

From Graph 1,

Thermocouple with ice-point, S = dv/dt

Gradient = (3.52 – 0) / (85 – 1.5)

= 0.04216 mV/⁰C

Thermocouple without ice-point, S = dv/dt

Gradient = (2.54 – 0) / (83.5 – 22)

= 0.04130 mV/⁰C

From Graph 2,

RTD, S = dv/dt

Gradient = (79.57 – 0) / (79.6 – 0)

= 0.9996 mV/⁰C

From Graph 3,

Thermistor, S = dv/dt

Gradient = (805 – 0) / (85 – 22.5)

= 12.88 mV/⁰C

From the sensitivity values obtained, we can see that thermistor has the highest sensitivity among all 4 temperature sensors and thermocouple has the lowest sensitivity value.

This means that for thermistor sensor, there will be a bigger jump in voltage for every degree Celsius increment. Having a larger sensitivity would enable one to detect small changes in temperature more accurately.

Temperature Coefficient of Resistance

For Thermistor,

β = -S(R_t + R₃)² / E_oR_tR₃

= -(12.88 x 10^-3)(30000 + 7599)² / (1.5 x 30000 x 7599)

= -53.25 x 10^-3 K^-1

For RTD,

β = S / (i x R_o)

= (0.9996 x 10^-3) / (2.1 x 10^-3 x 100)

= 4.76 x 10^-3 K^-1

The comparison of the magnitudes indicates that the thermistor possesses a higher temperature coefficient of resistance when compared to the RTD. This suggests that the thermistor undergoes a more substantial change in resistance for each unit change in temperature compared to the RTD. This reaffirms the earlier inference that the thermistor exhibits greater sensitivity than the RTD.

The anticipated temperature distribution is linear along the axial direction of the rod, assuming heat transfer exclusively in the axial direction due to circumferential insulation. With no heat generation within the rod and a constant temperature with respect to time, a linear temperature profile is expected.

However, the recorded temperature profile of the Perspex rod during the experiment demonstrates a non-linear relationship. This deviation may be attributed to Perspex's unique material properties, which impede heat conduction compared to other materials. It indicates the material's resistance to heat conductivity, resulting in an experimentally obtained hyperbolic temperature profile across the length of the rod rather than the anticipated linear relationship.

In a steady-state scenario, the temperature distribution typically tends toward linearity. This trend is observable when comparing the 15-minute graph to the 0-minute graph. However, the duration of the experiment is insufficient to achieve a full steady state, where temperature across the Perspex rod remains constant over time. Additionally, unaccounted heat losses due to radiation contribute to the observed non-linear relationship.

Relative % error of temperature deviation between surface temperature measurement

At 0 minute,

Temperature of the surface of the exposed end (embedded thermocouple) = 24.5⁰C

Surface Thermocouple wire = [(25 – 24.5) / 24.5] x 100%

= 2.04%

Surface RTD = [(25 – 24.5) / 24.5] x 100%

= 2.04%

Surface Thermistor = [(25 – 24.5) / 24.5] x 100%

= 2.04%

At 15 minute,

Temperature of the surface of the exposed end (embedded thermocouple) = 25.5⁰C

Surface Thermocouple wire = [(26.5 – 25.5) / 25.5] x 100%

= 3.92%

Surface RTD = [(27 – 25.5) / 25.5] x 100%

= 5.88%

Surface Thermistor = [(26 – 25.5) / 25.5] x 100%

= 1.96%

The primary objective of this laboratory experiment is to explore the sensitivity and accuracy of different temperature sensors, specifically a liquid-in-bulb thermometer and a surface thermistor. Through a comparative analysis of relative percent errors, this experiment aims to draw conclusions about the relationship between sensor sensitivity and accuracy.

Materials:

1. Liquid-in-bulb thermometer
2. Surface thermistor
3. Digital thermometer
4. Data logger
5. Insulation material
6. Stopwatch

Procedure:

1. Calibration of Sensors: a. Calibrate each temperature sensor to ensure accurate readings. b. Record the calibration values for later use in data analysis.
2. Temperature Measurement: a. Place the liquid-in-bulb thermometer and surface thermistor in a controlled environment. b. Record temperature readings at regular intervals using both sensors. c. Simultaneously, use the digital thermometer and data logger to obtain reference values.
3. Error Analysis: a. Calculate the relative percent error for each temperature sensor using the formula: Relative Percent Error (RPE)=∣Experimental Value−Reference ValueReference Value∣×100Relative Percent Error (RPE)=∣∣​Reference ValueExperimental Value−Reference Value​∣∣​×100

   b. Identify possible sources of errors, such as parallax errors, heat loss due to improper insulation, and fluctuations in readings.

   c. Discuss the impact of not recording readings at the 0-minute and 15-minute instants on the accuracy of the experiment.

   d. Analyze the fluctuations in readings and the influence of internal resistance within the wires on temperature measurements.

CONCLUSION

Calculations:

• Utilize the calibration values to adjust the readings and calculate corrected values for each sensor.

  Corrected Value=Raw Reading+Calibration OffsetCorrected Value=Raw Reading+Calibration Offset

Error Analysis:

• Discuss the impact of parallax errors on readings from the liquid-in-bulb thermometer.
• Explore how improper insulation might cause heat loss and affect the accuracy of the readings.
• Evaluate the significance of fluctuations in readings and the role of internal resistance in wires.

Improvements:

• Propose methods to eliminate parallax errors, such as using a digital thermometer.
• Suggest the use of a data logger to obtain readings simultaneously for all sensors, ensuring better synchronization.

Conclusion: Summarize the findings, highlighting the relative percent errors and the impact of different sources of errors on the experiment's accuracy. Discuss the relationship between sensor sensitivity and accuracy.

Appendix: Include the raw data, calculations, and any additional graphs or charts.

Acknowledgments: Recognize any assistance or guidance received during the experiment.

By following this comprehensive guide, you have conducted a thorough laboratory experiment on temperature sensors, error analysis, and potential improvements.

Calibrating various temperature sensors holds significant importance as it enables precise temperature readings in locations where traditional thermometers may be impractical. Each sensor possesses distinct characteristics such as sensitivity, temperature coefficient, response time, and accuracy. The experiment demonstrated that the thermistor exhibits greater sensitivity compared to the resistance thermometer, attributed to its higher temperature coefficient of resistance.

In terms of accuracy, deviation calculations revealed that the thermistor outperformed other sensors in the experiment. Through this study, we have gained insights into the unique characteristics of each sensor, enhancing our understanding of temperature measurement, especially concerning the surface temperature of a rod.