teaching-notes — Physics (THERMAL PHYSICS)

TOPIC: THERMAL PHYSICS SUBTOPIC: Measurement of Temperature SPECIFIC OUTCOMES: 1. Explain what temperature is. 2. Describe physical properties of substances which change with temperature. 3. Measure the temperature with thermometers. 4. Describe suitability of alcohol and mercury for use in liquid-in-glass thermometers. 5. Describe the relationship between the Celsius and Kelvin scales. INTRODUCTION Thermal physics is a branch of physics that deals with heat and temperature, and how they affect matter. Understanding temperature is fundamental to many scientific and everyday phenomena, from cooking to climate science. This unit will introduce the concept of temperature, how it is measured, the properties of substances that allow for its measurement, and the different temperature scales used in science. CORE CONCEPTS 1. What is Temperature? Temperature is a measure of the average kinetic energy of the particles (atoms or molecules) in a substance. When a substance is heated, its particles gain kinetic energy, vibrate or move faster, and its temperature increases. Conversely, when a substance is cooled, its particles lose kinetic energy, move slower, and its temperature decreases. Temperature indicates the degree of hotness or coldness of an object. The kinetic theory of matter states that: 1. All matter is made up of tiny particles (atoms, molecules, or ions). 2. These particles are in constant, random motion. 3. The degree of movement (kinetic energy) of these particles depends on their temperature. Higher temperature means faster movement and higher kinetic energy.

KINETIC THEORY OF MATTER: PARTICLE ARRANGEMENT AND MOVEMENT

✅ Check Your Understanding

Pause here. Let learners attempt these before moving on.

1. Quick Recall [1 mark]	Define temperature in terms of particle energy.
2. Apply the Concept [2 marks]	Explain why a hot object feels hotter than a cold object at the molecular level.
3. Misconception Check	True or False: Temperature is the total amount of heat energy in a substance. Justify your answer.

Answers

1. Temperature is a measure of the average kinetic energy of the particles in a substance.
2. A hot object has particles with higher average kinetic energy, causing them to vibrate or move faster. When touched, these rapidly moving particles transfer more energy to the particles in your hand, resulting in the sensation of heat.
3. False. Temperature is the average kinetic energy of particles, while heat is the total thermal energy transferred between objects due to a temperature difference.

2. Physical Properties of Substances Which Change with Temperature Many physical properties of substances change predictably with temperature. These changes form the basis of how thermometers work. Common properties that change with temperature include: • Volume (Thermal Expansion): Most substances expand when heated and contract when cooled. This is the most common thermometric property used in liquid-in-glass and bimetallic strip thermometers. Example:* Mercury or alcohol in a thermometer expands and rises in a capillary tube when heated. Railway lines have gaps to allow for thermal expansion during hot weather. • Density: As a substance expands when heated, its volume increases while its mass remains constant, leading to a decrease in density. Example:* Hot air is less dense than cold air, causing it to rise (convection). • Electrical Resistance: The electrical resistance of most metals increases with temperature. This property is used in resistance thermometers. Example:* Platinum resistance thermometers are used for precise temperature measurements in industrial settings. • Pressure of a Fixed Mass of Gas at Constant Volume: When a fixed mass of gas is heated in a constant volume container, the kinetic energy of its particles increases, leading to more frequent and forceful collisions with the container walls, thus increasing pressure. This is the principle behind gas thermometers. Example:* A gas thermometer uses the change in pressure of a fixed volume of gas to measure temperature. • Colour: Some substances change colour with temperature. This property is used in thermochromic materials. Example:* Thermochromic liquids or paints used in mood rings or kettles change colour at different temperatures. • Electromotive Force (e.m.f.): When two dissimilar metals are joined at two junctions and the junctions are kept at different temperatures, an electromotive force (voltage) is generated. This is known as the Seebeck effect and is used in thermocouples. Example:* Thermocouples are used to measure very high or rapidly changing temperatures in furnaces or engines.

✅ Check Your Understanding

Pause here. Let learners attempt these before moving on.

1. Quick Recall [1 mark]	Name two physical properties of a substance that change with temperature.
2. Apply the Concept [2 marks]	Explain how the principle of thermal expansion is applied in railway lines.
3. Misconception Check	True or False: All substances contract when heated. Justify your answer.

Answers

1. Volume, density, electrical resistance, pressure of a fixed gas, colour, electromotive force (any two).
2. Gaps are intentionally left between sections of railway lines. This allows the metal rails to expand safely during hot weather without buckling or deforming, preventing damage to the tracks.
3. False. Most substances expand when heated (thermal expansion). Contraction occurs when they are cooled. Water is a notable exception around 0°C to 4°C, where it contracts upon heating from 0°C to 4°C and then expands.

3. Measurement of Temperature with Thermometers A thermometer is an instrument used to measure temperature. It works by utilising a thermometric property, which is a physical property of a substance that changes predictably and measurably with temperature. Liquid-in-Glass Thermometer This is the most common type of thermometer. It consists of: • Bulb: A thin-walled glass reservoir at the bottom, containing the thermometric liquid (mercury or alcohol). • Capillary tube (bore): A very narrow glass tube extending from the bulb, through which the liquid expands and rises. • Stem: The thicker glass casing protecting the capillary tube. • Scale: Markings etched on the stem, indicating temperature values. Principle of Operation: When the bulb is heated, the liquid inside expands more than the glass bulb, causing it to rise up the narrow capillary tube. The height to which the liquid rises is proportional to the temperature.

STRUCTURE OF A LIQUID-IN-GLASS THERMOMETER

Calibration of Thermometers For a thermometer to give accurate readings, it must be calibrated. Calibration involves establishing a scale by identifying two fixed points: 1. Lower Fixed Point (Ice Point): This is the temperature at which pure ice melts or pure water freezes at standard atmospheric pressure (1 atmosphere). It is assigned a value of 0 °C. 2. Upper Fixed Point (Steam Point): This is the temperature at which pure water boils into steam at standard atmospheric pressure. It is assigned a value of 100 °C. Procedure for Calibration: • Place the thermometer in melting ice and mark the level of the liquid column. This is the 0 °C mark. • Place the thermometer in steam from boiling water and mark the level of the liquid column. This is the 100 °C mark. • The distance between these two marks is then divided into 100 equal divisions, with each division representing 1 °C.

CALIBRATION OF A LIQUID-IN-GLASS THERMOMETER

Worked Example: Thermometer Calibration A newly constructed liquid-in-glass thermometer has a liquid column length of 2.0 cm at the ice point and 18.0 cm at the steam point. If the liquid column measures 9.0 cm when immersed in a liquid, what is the temperature of the liquid in degrees Celsius?

Solution

Given:	L₀ = 2.0 cm (length at 0 °C), L₁₀₀ = 18.0 cm (length at 100 °C), L_T = 9.0 cm (length at unknown temperature T)
Find:	T = ? (°C)
Formula:	T = (L_T − L₀)(L₁₀₀ − L₀) × 100 °C
Substitute:	T = (9.0 − 2.0)(18.0 − 2.0) × 100 °C
Simplify:	T = 7.016.0 × 100 °C
Answer:	T = 43.75 °C

Worked Example: Calculating temperature using thermometer calibration

✅ Check Your Understanding

Pause here. Let learners attempt these before moving on.

1. Quick Recall [1 mark]	What are the two fixed points used in calibrating a Celsius thermometer?
2. Apply the Concept [3 marks]	A laboratory thermometer has a liquid column of 3.0 cm at 0 °C and 23.0 cm at 100 °C. What is the temperature when the liquid column is 15.0 cm long?
3. Misconception Check	A student states that a thermometer can be calibrated using only one fixed point. Is this statement true or false? Justify your answer.

Answers

1. The lower fixed point (ice point) at 0 °C and the upper fixed point (steam point) at 100 °C.
2.

Given: L₀ = 3.0 cm, L₁₀₀ = 23.0 cm, L_T = 15.0 cm
Find: T = ? (°C)
Formula: T = (L_T − L₀)(L₁₀₀ − L₀) × 100 °C
Substitute: T = (15.0 − 3.0)(23.0 − 3.0) × 100 °C = 12.020.0 × 100 °C
Answer: T = 60 °C

3. False. Two fixed points are essential for calibration to define both the starting point (zero) and the size of each degree interval on the scale. A single fixed point would only establish one reference, but not the range or division size.

4. Suitability of Alcohol and Mercury for Use in Liquid-in-Glass Thermometers Both mercury and alcohol are commonly used in liquid-in-glass thermometers due to their suitable thermometric properties.

Comparison: Mercury vs. Alcohol as Thermometric Liquids

Property	Mercury	Alcohol (e.g., Ethanol)
Freezing Point	−39 °C (good for most ambient temperatures)	−115 °C (suitable for very low temperatures, e.g., polar regions)
Boiling Point	357 °C (good for high temperatures)	78 °C (low, limiting its use for high temperatures)
Expansion	Expands uniformly (regular expansion), making it accurate.	Expands non-uniformly at very high temperatures, slightly less accurate for precision.
Visibility	Silvery and opaque, easily visible.	Colourless, usually dyed red or blue for visibility.
Wetting of Glass	Does not wet (stick to) glass, ensuring accurate readings.	Wets glass, can leave residue and affect accuracy.
Thermal Conductivity	Good thermal conductor, responds quickly to temperature changes.	Poor thermal conductor, responds slower to temperature changes.
Toxicity	Highly toxic if ingested or inhaled as vapour.	Less toxic than mercury, safer for general use.

Figure: Comparing mercury and alcohol as thermometric liquids

Summary of Suitability: • Mercury is generally preferred for laboratory and clinical thermometers due to its wide temperature range, uniform expansion, high visibility, and good thermal conductivity, allowing for quick and accurate measurements. However, its toxicity is a disadvantage. • Alcohol thermometers are useful for measuring very low temperatures where mercury would freeze. They are also safer and cheaper, making them suitable for educational and outdoor use despite their slower response and lower boiling point.

✅ Check Your Understanding

Pause here. Let learners attempt these before moving on.

1. Quick Recall [1 mark]	State one advantage of using mercury over alcohol in a liquid-in-glass thermometer.
2. Apply the Concept [2 marks]	Explain why an alcohol thermometer would be more suitable than a mercury thermometer for measuring temperatures in a very cold environment, such as the Antarctic.
3. Misconception Check	A student claims that mercury is a better thermometric liquid than alcohol because it is colourless and therefore more transparent. Is this statement true or false? Justify your answer.

Answers

1. Mercury has a higher boiling point, expands more uniformly, does not wet glass, or is a better thermal conductor (any one).
2. Mercury freezes at -39 °C, which is a relatively high temperature for very cold environments. Alcohol, with a much lower freezing point of -115 °C, would remain liquid and functional in temperatures where mercury would solidify, making it suitable for such conditions.
3. False. Mercury is silvery and opaque, making it highly visible. Alcohol is colourless and usually dyed to improve visibility. The student's claim about mercury being colourless is incorrect.

5. Relationship Between the Celsius and Kelvin Scales There are several temperature scales, but the two most commonly used in science are the Celsius (°C) scale and the Kelvin (K) scale. • Celsius Scale: This is a relative temperature scale where 0 °C is the freezing point of water and 100 °C is the boiling point of water at standard atmospheric pressure. • Kelvin Scale (Absolute Temperature Scale): This is the SI unit of temperature. It is an absolute scale, meaning 0 K represents absolute zero, the theoretical lowest possible temperature where particles have minimum kinetic energy. There are no negative temperatures on the Kelvin scale. Absolute Zero: • 0 K is equivalent to −273.15 °C (often approximated as −273 °C for calculations). • At absolute zero, the particles of a substance have the minimum possible kinetic energy; it is not a state of complete lack of thermal energy but the lowest possible energy state. Relationship and Conversion Formula: The size of one degree Celsius is exactly equal to the size of one Kelvin. The only difference is the starting point (zero). To convert between Celsius and Kelvin:

Key Formulas: Temperature Conversion

Celsius to Kelvin	T_K = T_°C + 273
Kelvin to Celsius	T_°C = T_K − 273

T_K = temperature in Kelvin (K) | T_°C = temperature in degrees Celsius (°C)

Figure: Formulas for converting between Celsius and Kelvin scales

CELSIUS AND KELVIN TEMPERATURE SCALES COMPARISON

Worked Example 1: Converting Celsius to Kelvin Convert a temperature of 25 °C to Kelvin.

Solution

Given:	T_°C = 25 °C
Find:	T_K = ? (K)
Formula:	T_K = T_°C + 273
Substitute:	T_K = 25 + 273
Answer:	T_K = 298 K

Worked Example: Converting temperature from Celsius to Kelvin

Worked Example 2: Converting Kelvin to Celsius A process operates at a temperature of 300 K. What is this temperature in degrees Celsius?

Solution

Given:	T_K = 300 K
Find:	T_°C = ? (°C)
Formula:	T_°C = T_K − 273
Substitute:	T_°C = 300 − 273
Answer:	T_°C = 27 °C

Worked Example: Converting temperature from Kelvin to Celsius

✅ Check Your Understanding

Pause here. Let learners attempt these before moving on.

1. Quick Recall [1 mark]	What is the SI unit of temperature?
2. Apply the Concept [2 marks]	A substance has a temperature of −15 °C. What is this temperature in Kelvin?
3. Misconception Check	True or False: A temperature change of 10 °C is equivalent to a temperature change of 10 K. Justify your answer.

Answers

1. Kelvin (K).
2.

Given: T_°C = −15 °C
Find: T_K = ? (K)
Formula: T_K = T_°C + 273
Substitute: T_K = −15 + 273
Answer: T_K = 258 K

3. True. The size of one degree Celsius is exactly equal to the size of one Kelvin. Therefore, a change of 10 units on either scale represents the same magnitude of temperature change.

SUMMARY Temperature is a fundamental concept in physics, defined as the average kinetic energy of the particles within a substance, indicating its degree of hotness or coldness. Various physical properties, such as volume, density, electrical resistance, and pressure, change predictably with temperature and are exploited in different types of thermometers. The liquid-in-glass thermometer, using either mercury or alcohol, is a common device, calibrated using the ice point (0 °C) and steam point (100 °C). Mercury offers advantages like a wide range and uniform expansion, while alcohol is suited for very low temperatures. The Kelvin scale is the SI unit for temperature and is an absolute scale, related to Celsius by the formula T_K = T_°C + 273. ASSESSMENT QUESTIONS 1. Define temperature and state its SI unit. [2 marks] 2. Describe how the kinetic theory of matter explains the concept of temperature. [2 marks] 3. Name three physical properties of substances that can be used to measure temperature. [3 marks] 4. Explain the principle of operation of a liquid-in-glass thermometer. [2 marks] 5. A student calibrates a new thermometer and finds that the length of the mercury column is 1.5 cm at the ice point and 16.5 cm at the steam point. (a) What is the range of the thermometer in terms of length? [1 mark] (b) If the mercury column is 9.0 cm long when placed in a hot liquid, what is the temperature of the liquid in °C? [3 marks] 6. State two advantages of using mercury over alcohol in a liquid-in-glass thermometer. [2 marks] 7. State two advantages of using alcohol over mercury in a liquid-in-glass thermometer. [2 marks] 8. Convert the following temperatures: (a) 37 °C to Kelvin. [2 marks] (b) 280 K to Celsius. [2 marks] 9. Explain what is meant by "absolute zero" and its value on both the Celsius and Kelvin scales. [3 marks] 10. Why is the Kelvin scale considered an absolute temperature scale, unlike the Celsius scale? [2 marks] COMMON DIFFICULTIES & MISCONCEPTIONS • Heat vs. Temperature: Students often confuse heat and temperature. Heat is the total thermal energy transferred, while temperature is the average kinetic energy of particles. • Absolute Zero: Misunderstanding that 0 K means no particle motion. It means minimum possible kinetic energy, not zero. • Conversion Formula: Forgetting whether to add or subtract 273, especially with negative Celsius temperatures. Some might mistakenly use 273.15 instead of the simplified 273 for general calculations. • Properties of Liquids: Not remembering specific properties (e.g., wetting, thermal conductivity, freezing/boiling points) for mercury vs. alcohol. • Calibration: Thinking that 0 °C or 100 °C are arbitrary numbers, rather than scientifically defined fixed points based on phase changes of water. • Uniform Expansion: Assuming all liquids expand uniformly, which is not entirely true (e.g., alcohol is less uniform at extremes than mercury). QUICK REFERENCE SUMMARY

Key Terms & Formulas: Measurement of Temperature

Temperature	Measure of the average kinetic energy of particles in a substance. SI unit: Kelvin (K).
Thermometric Property	Physical property of a substance that changes predictably with temperature (e.g., volume, resistance, pressure).
Fixed Points	Standard reference temperatures for calibration: Ice Point (0 °C) and Steam Point (100 °C).
Absolute Zero	Lowest theoretical temperature, 0 K or −273 °C. Particles have minimum kinetic energy.
Celsius to Kelvin	T_K = T_°C + 273
Kelvin to Celsius	T_°C = T_K − 273
Calibration Formula	T = (L_T − L₀)(L₁₀₀ − L₀) × 100 °C

Figure: Summary of key terms and formulas for temperature measurement

teaching-notes — Physics (THERMAL PHYSICS)

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