teaching-notes — Physics (THERMAL PHYSICS)

Topic: THERMAL PHYSICS

Subtopic: Measurement of Temperature

MEANING OF TEMPERATURE

Definition: Temperature is a measure of the average kinetic energy of the particles of a substance. When particles move faster on average, the temperature is higher.

Explanation: In a solid the particles vibrate about fixed positions and have lower average kinetic energy. In a liquid particles move more freely and have greater average kinetic energy. In a gas particles move fastest and have the highest average kinetic energy. Temperature tells us how hot or cold a body is and determines the direction of heat flow (from higher temperature to lower temperature).

Example: If two bodies are in contact and their particle speeds are different, energy transfers until the average kinetic energies (temperatures) are equal.

simple labelled pupil-notebook diagram of particle motion in...

PHYSICAL PROPERTIES THAT CHANGE WITH TEMPERATURE

Many physical properties vary when temperature changes. Knowing these changes helps us measure temperature and predict behaviour of materials.

Property	How it changes with temperature	Example / Use
Density	Generally decreases as temperature increases (materials expand).	Warm air rises because its density is lower than cold air.
Electrical resistance	In most metals resistance increases with temperature; in some semiconductors resistance decreases with temperature.	Resistance thermometers (RTDs) use the change in resistance to measure temperature.
Length / Volume (thermal expansion)	Objects expand in length and volume when heated and contract when cooled.	Allowance for expansion in bridge joints and railway lines.
Pressure (for gases at constant volume)	Pressure increases with temperature if volume is fixed (particles collide more often and with greater force).	Pressure gauges can indicate temperature change in sealed containers.
Colour / Emission	Hot objects change colour (black-body radiation) as temperature rises.	Pyrometry uses colour to estimate very high temperatures.

simple labelled pupil-notebook diagram of a metal rod before...

MEASUREMENT OF TEMPERATURE AND CALIBRATION OF THERMOMETERS

Thermometers measure temperature by using a physical property that changes with temperature. Common types: liquid-in-glass (mercury or alcohol), resistance thermometers (RTD), thermocouples, and bimetallic strips.

Liquid-in-glass thermometers: Contain a liquid that expands with temperature. The scale on the glass shows temperature readings.

Resistance thermometers (RTDs): Use the increase of electrical resistance with temperature (usually of platinum) to give accurate readings.

Thermocouples: Two different metals joined at one end produce a voltage that depends on temperature; the voltage is measured and converted to temperature.

Calibration of thermometers

Calibration adjusts the thermometer scale so readings match known fixed temperatures. Two standard fixed points are used:

Ice point (melting point of pure ice) — defined as 0 °C.
Steam point (boiling point of pure water at standard pressure 1 atm) — defined as 100 °C.

Calibration procedure (simple two-point linear calibration): Place the thermometer in an ice-water mixture and note the reading R_ice. Place it in boiling water and note the reading R_steam. If the thermometer scale is linear, convert any reading R to the true temperature T using a linear relation found from the two fixed points.

Worked example 1 (Conversion between Celsius and Kelvin)

A laboratory thermometer shows a temperature of 25.0 °C. Convert this temperature to kelvin.

Solution

Given:	T = 25.0 °C
Find:	T (in K) = ?
Formula:	T (K) = T (°C) + 273.15
Substitute:	T (K) = 25.0 + 273.15
Answer:	T = 298.15 K

Worked Example: Converting Celsius to Kelvin

Worked example 2 (Two-point linear calibration)

A new liquid-in-glass thermometer gives a reading of 1.2 °C in a mixture of melting ice and 101.6 °C in boiling water at the laboratory. What is the true temperature when this thermometer reads 25.0 °C? Assume the thermometer scale is linear.

Solution

Given:	R_ice = 1.2 °C (should be 0.0 °C), R_steam = 101.6 °C (should be 100.0 °C)
Find:	True temperature T when reading R = 25.0 °C
Formula:	Assume linear relation: T = m·R + c. Use fixed points to find m and c.
Work:	Step 1: For ice point: 0 = m·1.2 + c → c = −1.2m. Step 2: For steam point: 100 = m·101.6 + c. Substitute c: 100 = m·101.6 − 1.2m = m·(101.6 − 1.2) = m·100.4. So m = 100 / 100.4 = 0.9960159 (approx). Then c = −1.2 × 0.9960159 = −1.1952191 (approx). Step 3: For R = 25.0 °C: T = 0.9960159 × 25.0 − 1.1952191 = 23.70518 °C (approx).
Answer:	True temperature ≈ 23.71 °C

Worked Example: Calibration using ice and steam fixed points

simple labelled pupil-notebook diagram of thermometer calibr...

USING THERMOMETERS: PRACTICAL POINTS

Always allow the thermometer to reach thermal equilibrium with the object or medium before reading.
Read the thermometer at eye level to avoid parallax error.
For liquid-in-glass thermometers, note the bottom of the meniscus.
Do not use a mercury thermometer if it is broken; mercury is toxic.

KEY TERMS

Term	Meaning
Temperature	Measure of average kinetic energy of particles (units: °C, K).
Thermometer	Device that measures temperature using a property that changes with temperature.
Calibration	Adjustment or checking of a measuring instrument against known standards (fixed points).
Fixed points	Temperatures with well-known values used for calibration (e.g., 0 °C and 100 °C).

SUMMARY

Temperature measures average particle kinetic energy. Physical properties such as density, electrical resistance, and length change with temperature and can be used to build thermometers. Thermometers must be calibrated using fixed points (ice point and steam point) and may require a linear correction if the scale is not exact.

REVISION QUESTIONS

1.	State what temperature measures.
2.	Give two physical properties that change with temperature and give one practical use for each.
3.	Convert 310 K to °C.
4.	Why are the ice point and steam point used for calibration?
5.	A metallic rod length increases when heated. Explain this in terms of particle motion.
6.	What reading error is caused by parallax and how can it be avoided?
7.	A thermometer reads 5.0 °C in an ice bath. Suggest a simple correction to apply to readings.
8.	Explain why resistance thermometers are more suitable for precise laboratory work than simple liquid-in-glass thermometers.

PRACTICE EXERCISE

1.	Convert 0.0 °C to kelvin.
2.	A thermometer reads 2.0 °C in ice and 102.0 °C in steam. What is the true temperature when it reads 20.0 °C? (Assume linear scale.)
3.	Name one advantage and one disadvantage of a liquid-in-glass thermometer.
4.	A sealed gas thermometer at constant volume shows pressure proportional to temperature. If pressure doubles, what happens to the absolute temperature?
5.	A metal wire of length 1.000 m at 20 °C expands to 1.0012 m at 30 °C. Calculate the change in length and state which property this illustrates.
6.	Explain briefly how a thermocouple gives a measure of temperature.

ANSWERS TO PRACTICE EXERCISE

Q	Answer with working
1.	Work: T(K) = T(°C) + 273.15 Substitute: T(K) = 0.0 + 273.15 Answer: 273.15 K
2.	Work: Let T = m·R + c. Ice: 0 = m·2.0 + c → c = −2.0m. Steam: 100 = m·102.0 + c → 100 = m(102.0 − 2.0) = m·100.0 → m = 100/100 = 1.0. Then c = −2.0 × 1.0 = −2.0. For R = 20.0: T = 1.0×20.0 − 2.0 = 18.0 °C. Answer: 18.0 °C
3.	Answer: Advantage: Simple and inexpensive; easy to read. Disadvantage: Slower response and less accurate than electrical thermometers; mercury is toxic if broken.
4.	Work: At constant volume for an ideal gas, pressure ∝ absolute temperature (Kelvin): P ∝ T. If pressure doubles, absolute temperature doubles. Answer: The absolute temperature doubles.
5.	Work: Change in length ΔL = 1.0012 m − 1.000 m = 0.0012 m = 1.2 mm. This illustrates thermal expansion (increase of length with temperature). Answer: ΔL = 0.0012 m (1.2 mm); property = thermal expansion.
6.	Answer: A thermocouple joins two different metals; the junction at a temperature produces an emf (voltage) that depends on temperature. Measuring the emf and using a calibration table gives the temperature.

teaching-notes — Physics (THERMAL PHYSICS)

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