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Physics 001.001.004 Kelvin

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Physics 001.001.004 Kelvin

Alignment

Learning Intentions

By the end of the lesson, students will be able to:

  • Use to convert temperature measurements from degrees Celsius to kelvin.
  • Rearrange to convert from kelvin to degrees Celsius.
  • Explain why kelvin is the SI unit for thermodynamic temperature.
  • Discuss temperature as a state variable that describes the thermal condition of a system at a particular state.
  • Distinguish between a temperature value and a temperature change.

Success Criteria

By the end of the lesson, students have successfully:

  • Converted temperatures between Celsius and kelvin with correct units.
  • Identified physically impossible Kelvin temperatures below .
  • Explained that temperature is a state variable because it depends only on the present thermal state of a system, not the path taken to reach that state.
  • Used in simple physics contexts involving room temperature, boiling water, freezing water and absolute zero.
  • Recognised that a change of is equal in size to a change of .

Syllabus Reference

  • Unit 1: Thermal, Nuclear and Electrical Physics
  • Topic 1: Heating Processes
  • Science Understanding: Use to convert temperature measurements.
  • Science Inquiry: Use measuring devices to collect data, ensuring measurements are recorded using the correct symbol, SI unit, number of significant figures and associated measurement uncertainty.

Phenomenon

A digital thermometer reads in the classroom. A physics data table, however, asks for temperature in kelvin.

Students are asked:

Why do physicists often use kelvin instead of Celsius, and what does the temperature of the room tell us about the current state of the air?

Demonstration options:

  • Display room temperature on a digital thermometer in .
  • Ask students to convert it to kelvin using .
  • Compare common reference temperatures:
    • Freezing point of water:
    • Room temperature: approximately
    • Boiling point of water:
    • Absolute zero:

Key Idea

Temperature describes the thermal state of a system. In physics, temperature is often measured in kelvin because kelvin begins at absolute zero, where particles have minimum possible thermal motion.

The conversion used in this course is:

where:

  • is temperature in kelvin.
  • is temperature in degrees Celsius.

To convert from kelvin to Celsius:

Concept

The concept and thought that best describes the cause of the phenomenon is below.

Temperature is a measure related to the average kinetic energy of particles in a system. A higher temperature means, on average, particles have greater kinetic energy.

Temperature is also a state variable. A state variable describes the condition of a system at a particular moment. It depends only on the current state of the system, not on the path taken to reach that state.

For example, a cup of water at has the same temperature state whether it:

  • cooled down from , or
  • warmed up from .

The final temperature is a property of the current state of the water. The path taken to reach that temperature does not change the value of the temperature.

Other thermodynamic state variables include:

  • pressure
  • volume
  • internal energy
  • temperature

Temperature is an intensive state variable because it does not depend on the amount of substance. A small cup of water and a large bucket of water can both have a temperature of .

Convention

The key conventions associated with the concept and in the branch of established knowledge is below.

  • The SI unit for temperature is kelvin, symbol .
  • Kelvin is written without a degree symbol.
    • Correct:
    • Incorrect:
  • Celsius uses the degree symbol.
    • Correct:
  • The QCAA formula for this topic is .
  • A more precise conversion uses , but in this course we use unless greater precision is required.
  • There are no negative Kelvin temperatures in ordinary thermodynamics because represents absolute zero.
  • A temperature interval has the same size in Celsius and kelvin:
    • A change of equals a change of .
    • Therefore, .

Example:

Water warms from to .

In kelvin:

The temperature change is the same size.

Misconceptions

Common misconceptions students have regarding the concept when applying to various situations and solving problems. It could be a conceptual, mathematical or logical misconception.

  • Students may write kelvin with a degree symbol, such as , instead of .
  • Students may think means no thermal energy. In fact, , so particles still have thermal motion.
  • Students may subtract when converting from Celsius to kelvin instead of adding .
  • Students may think a temperature change must be converted by adding . This is incorrect. A change of is a change of .
  • Students may confuse temperature with heat. Temperature is a state variable. Heat is energy transferred due to a temperature difference.

Further Reading

  • QCAA Physics Unit 1: Heating Processes
  • SI base units and the kelvin
  • Kinetic particle model of matter
  • Thermal equilibrium
  • First law of thermodynamics and state variables

Explicit Instruction

Teacher explanation sequence:

  1. Celsius and kelvin measure temperature using scales with equal-sized divisions.
  2. Celsius is based around common water reference points:
    • is approximately the freezing point of water.
    • is approximately the boiling point of water at standard pressure.
  3. Kelvin begins at absolute zero:
  4. Because kelvin starts units below Celsius:

  1. To reverse the conversion:

  1. Temperature is a state variable:
    • It describes the present thermal state of a system.
    • It does not describe how the system reached that state.
    • It can be used with other state variables, such as pressure and volume, to describe a thermodynamic system.

Class discussion:

A sealed gas cylinder has a temperature of .

Ask:

  • What is this temperature in Celsius?
  • Does this temperature tell us whether the gas was heated, cooled or compressed to reach this state?
  • What additional information would we need to describe the state of the gas more completely?

Expected discussion:

  • Temperature alone does not reveal the path taken.
  • Pressure, volume and amount of gas may also be needed.

Worked Examples

Worked Example 1

Convert to kelvin.

Formula:

Substitute:

Solve:

Answer:

Worked Example 2

Convert to degrees Celsius.

Formula:

Substitute:

Solve:

Answer:

Worked Example 3

A sample of water warms from to .

Part A: Convert both temperatures to kelvin.

Initial temperature:

Final temperature:

Part B: Determine the temperature change.

In Celsius:

In kelvin:

Answer:

The temperature change is or . Temperature intervals have the same size in Celsius and kelvin.

Check for Understanding

Check 1

Convert to kelvin.

Solution:

Check 2

Convert to degrees Celsius.

Solution:

Check 3

A student says:

The temperature increased by , so in kelvin the increase is .

Explain the error.

Solution:

The student has confused a temperature value with a temperature change. The formula is used for converting temperature readings, not temperature intervals.

A change of is equal in size to a change of .

Investigation (Alternative to Explicit)

Hypothesis

If the temperature of a system is measured in Celsius and then converted to kelvin, then each kelvin value will be exactly greater than the Celsius value, while the size of any temperature change will remain the same.

Data Collection

Equipment:

  • digital thermometer or temperature probe
  • beakers
  • cold water
  • room-temperature water
  • warm water
  • ice
  • kettle or hot water source controlled by teacher
  • safety glasses

Method:

  1. Measure the temperature of cold water in .
  2. Measure the temperature of room-temperature water in .
  3. Measure the temperature of warm water in .
  4. Record each measurement with appropriate units and uncertainty.
  5. Convert each measurement to kelvin using .
  6. Calculate the temperature change between cold and warm samples in both Celsius and kelvin.

Suggested data table:

SampleTemperature in Temperature in Measurement uncertainty
Cold water
Room-temperature water
Warm water

Analysis

Students answer:

  1. Was each kelvin value greater than the Celsius value?
  2. Did the temperature change have the same numerical value in Celsius and kelvin?
  3. Which measured temperature represents the thermal state of the water sample?
  4. Does the final temperature tell you whether the water was heated quickly or slowly?
  5. Why is temperature a state variable?

Expected conclusion:

Temperature is a state variable because it describes the present thermal condition of a system. The measured temperature does not depend on whether the system reached that temperature by heating, cooling or mixing.

Evaluation

Students evaluate:

  • Was the thermometer precise enough for the measurements?
  • Was the water temperature uniform throughout the beaker?
  • Was there heat transfer between the water and the surroundings?
  • How could stirring affect the reliability of the temperature measurement?
  • Why should measurements include units and uncertainty?

Problems

The following problems are designed to develop fluency with Celsius to kelvin conversion, kelvin to Celsius conversion, and temperature as a state variable.

  1. Convert to kelvin.

  2. Convert to kelvin.

  3. Convert to kelvin.

  4. Convert to degrees Celsius.

  5. Convert to degrees Celsius.

  6. Convert to degrees Celsius.

  7. A thermometer reads . What is this temperature in kelvin?

  8. A gas sample has a temperature of . What is this temperature in degrees Celsius?

  9. A cup of tea cools from to . What is the temperature change in Celsius and kelvin?

  10. A student records the temperature of a metal block as . Another student records the same state as . Are the students describing the same thermal state? Explain.

  11. Explain why is not a physically valid temperature in this course.

  12. A sample of water is at . Explain why this temperature is a state variable, even if the water could have reached this temperature by different processes.

Answers:

  10. Yes. , so both students are describing the same temperature state.
  11. Kelvin begins at absolute zero. Temperatures below are not physically valid in ordinary thermodynamics.
  12. Temperature is a state variable because it describes the current thermal state of the water. It does not depend on whether the water was heated from a lower temperature or cooled from a higher temperature.

Followup

Self-check

Students should be able to answer:

  • Can I convert from Celsius to kelvin using ?
  • Can I convert from kelvin to Celsius using ?
  • Do I remember that kelvin does not use a degree symbol?
  • Can I explain why a temperature change of is the same size as a temperature change of ?
  • Can I explain why temperature is a state variable?
  • Can I distinguish between temperature and heat?

Exit ticket:

  1. Convert to kelvin.
  2. Convert to degrees Celsius.
  3. Explain in one sentence why temperature is a state variable.

Expected answers:

  3. Temperature is a state variable because it describes the current thermal state of a system and does not depend on the path taken to reach that state.

Next Topic

Explain that a change in temperature is due to the addition or removal of energy from a system without phase change, leading into specific heat capacity and the equation .

Graph View