# UTPA STEM/CBI Courses/Measurements and Instrumentation/Temperature Measurement

Course Title: Measurements
Lecture Topic: Temperature Measurement
Instructor: Dr. Stephen Crown
Institution: University of Texas - Pan American

## Backwards Design

Course Objectives
* Primary Objectives- By the next class period students will be able to:
** Differentiate between zero-, first-, and second-order systems
** Understand first-order step functions
** Derive a time constant
* Sub Objectives- The objectives will require that students be able to:
** Understand several heat transfer/thermodynamics equations
** Solve a differential equation
* Difficulties- Students may have difficulty:
** Remembering heat transfer/thermodynamics equation
** Remembering how to solve the differential equations
* Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
** Understanding how thermometers work
** Understanding how measuring systems behave
Model of Knowledge
* Concept Map
** Understand equations
** Formulate ideas
** Express ideas
* Content Priorities
** Enduring Understanding
*** Understand how step-functions work
** Important to Do and Know
*** Understand the correlation between various classes
*** Formulate ideas based on knowledge previously obtained
** Worth Being Familiar with
*** Differential Equations
*** Thermodynamics
*** Heat Transfer
Assessment of Learning
* Formative Assessment
** In Class (groups)
*** Generate equation to solve for thermometer output
** Homework (individual)
*** Pre-lecture quiz after student has read chapter
* Summative Assessment
** In class quiz over lesson

## Legacy Cycle

Students will be asked to read chapter 3 of their measurements book prior to this lesson. They will also be provided with a temperature measurement quiz online so that they may evaluate their own understanding of the topic prior to attending class.
OBJECTIVE
By the next class period, students will be able to:
* Differentiate between zero-, first-, and second-order systems
* Understand first-order step functions
* Derive a time constant
The objectives will require that students be able to:
* Understand several heat transfer/thermodynamics equations
* Solve a differential equation
THE CHALLENGE
The students will be presented with the following questions:
* Why is it that when taking ones temperature with a glass mercury thermometer it is recommended that the thermometer stay in the mouth for at least three minutes?
* Is three minutes a sufficient amount of time?
* Can this time be reduced while maintianing accuracy in measurement?
GENERATE IDEAS
The students will be given a few minutes to individually write down their answers to the questions that have been presented. Students may respond with answers such as:
* It takes the thermometer time to reach steady state
* Because of the the reaction time of the thermometer
* Because of the thermometer's time constant, you want an accurate reading
MULTIPLE PERSPECTIVES
The professor will lecture on first-order step functions so that students will gain a better understanding of the topic. Students will be asked, "What do we need to know in order to answer our challenge questions?" and given a few minutes to individually write down their responses. Examples include:
* We need to know the materials of the thermometer and their properties
* We need to know some heat transfer, thermodynamics, and differential equation
RESEARCH & REVISE
Students will be provided with heat transfer and thermodynamics equations. They will then form groups and be asked to begin deriving the time constant.
TEST YOUR METTLE
Students will receive feedback on their progress and ideas as well as the correct process for deriving the desired equation. Students will be presented with a quiz at the beginning of the following class.
GO PUBLIC
Students will now be able to answer the questions presented at the beginning of the lesson and will be asked to turn in a brief explanation.

## Pre-Lesson Quiz

Multiple Choice.
1. In temperature measurement, the body temperature is constant yet the signal to the thermometer is changing from the room temperature to the body temperature. This can be classified as _____.
a) a static measurement
b) a dynamic measurement
c) a step change
d) a dynamic measurement and a step change
e) a static measurement and a dynamic measurement
2. A thermometer is an example of a _____.
a) zero-order system
b) first-order system
c) second-order system
d) all of the above
e) none of the above
3. How often is the exact input-output relationship of a system found from calibration?
a) always
b) 98% of the time
c) 50% of the time
d) 33.3% of the time
e) never
4. What affects the time constant of a thermometer?
a) the mass of the liquid inside the thermometer
b) the specific heat of the liquid inside the thermometer
c) the heat transfer coefficient between the thermometer and the environment
d) all of the above
e) none of the above
5. The time constant is the time required for a first-order system to achieve __% of the step change magniture.
a) 33.4
b) 63.2
c) 86.5
d) 95
e) 99.2
True or False
6. A measurement system will always output information.
7. The thermometer must gain energy from its new environment to reach thermal equilibrium, and this takes an infinite amount of time.
8. The output signal obtained depends on the initial conditions as well as the input signal placed on the measurement system.
9. The time constant provides a measusre of the speed of the system response, and as such is an importanct specificcation in measuring dynamic input signals.
10. One must wait 3 time constants for a first-order system response to be 95% accurate.
11. A first-order system takes an infite amount of time to be 100% accurate.
12. All glass-mercury thermometers have the same time constant.

## Test Your Mettle Quiz

Answer the following questions to determine your skill level.
NOVICE
A glass thermometer with a time constant of 30 seconds and initially at room temperature (T=20°C) is used to measure the constant temperature of still air in an oven (T=100°C). What temperature is indicated on the thermometer 30 seconds after being placed in the oven?
PRACTITIONER
A glass thermometer, initially at room temperature (T=20°C), is used to measure the constant temperature of still air in an oven (T=100°C). Thirty seconds after being placed in the oven the thermometer reads 35°C . What is the time constant of the thermometer?
MASTER
A glass thermometer, initially at room temperature (T=20°C), is used to measure the constant temperature of still air in an oven. Thirty seconds after being placed in the oven the thermometer is removed. Thirty seconds after it has been removed the thermometer reads 35°C. What is the temperature of the oven?