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Karnataka Board PUCPUC Science Class 11
Textbook Solutions12072
Concept Notes & Videos318
Syllabus

Measurement of Temperature

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Topics

Estimated time: 28 minutes
  • Definition: Adiabatic Wall
  • Definition: Diathermic Wall
  • Definition: Thermal Equilibrium
  • Definition: Thermometry
  • Law: Zeroth Law of Thermodynamics
  • Temperature Scales
  • Conversion Formulas
  • Thermometers Use the Zeroth Law
  • Thermometric Property
  • Types of Thermometers
  • Characteristics of a Good Thermometer
  • Example 1
  • Example 2
  • Example 3
  • Example 4
  • Summary
Maharashtra State Board: Class 11

Definition: Adiabatic Wall

An adiabatic wall is an ideal partition that completely prevents heat transfer between two systems. In diagrams, it is shown as a thick, cross-hatched (slanting lines) region.

Maharashtra State Board: Class 11

Definition: Diathermic Wall

A diathermic wall is a partition that freely allows heat to flow between two systems. It is shown as a thin dark line in diagrams. A thin copper sheet is a good example.

Maharashtra State Board: Class 11

Definition: Thermal Equilibrium

When two bodies at different temperatures are brought into contact through a diathermic wall, heat flows from the hotter body to the cooler one. This continues until both reach the same temperature, at which point heat flow stops. This state is called thermal equilibrium.

Maharashtra State Board: Class 11

Definition: Thermometry

Thermometry is the branch of physics dealing with temperature measurement. It relies on the principle that certain physical properties of materials change continuously and predictably with temperature.

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Law: The Zeroth Law of Thermodynamics

If system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then systems A and B are in thermal equilibrium with each other.

Maharashtra State Board: Class 11

Temperature Scales

To measure temperature, we need a scale — a system of numbers tied to fixed reference points. Three scales are widely used in science.

Fixed Reference Points

Reference Point Description Celsius (°C) Fahrenheit (°F) Kelvin (K)
Ice Point Freezing point of pure water at 1 atm 0 °C 32 °F 273.15 K
Steam Point The boiling point of pure water at 1 atm 100 °C 212 °F 373.15 K
Absolute Zero Lowest possible temperature −273.15 °C −459.67 °F 0 K

The Three Scales Compared

Feature Celsius (°C) Fahrenheit (°F) Kelvin (K)
Named after Anders Celsius (1701–1744) Daniel G. Fahrenheit (1686–1736) Lord Kelvin (1824–1907)
Ice point 0 32 273.15
Steam point 100 212 373.15
Divisions between 100 180 100
Degree size Same as 1 K 5/9 of 1 °C (smaller) Same as 1 °C
Common use Most countries, science USA, some Caribbean nations SI unit – scientific calculations
Can it be negative? Yes Yes

No (starts at absolute zero)

Visual: Side-by-Side Temperature Scales

Fig.: Three temperature scales side by side — showing ice point, steam point, room temperature (27°C), and body temperature (37°C).

Maharashtra State Board: Class 11

Conversion Formulas

Master Conversion Formula:

\[\frac{T_F-32}{180}=\frac{T_C}{100}\] = \[\frac {T_K−273.15}{100}\]

Conversion Formula
Celsius → Fahrenheit TF = \[\frac{9}{5}\] × TC + 32
Fahrenheit → Celsius TC = \[\frac{5}{9}\] × (TF - 32)
Celsius → Kelvin TK = TC + 273.15)
Kelvin → Celsius TC = TK - 273.15)
Thermometric Property T = 100 × \[\frac{(P_T-P_1)}{(P_2-P_1)}\]
Maharashtra State Board: Class 11

Thermometers Use the Zeroth Law

When a doctor places a mercury thermometer in your mouth:

  1. Initially, your body (at a higher temperature) transfers heat to the mercury (at a lower temperature).
  2. After some time, the mercury and your body reach thermal equilibrium — the mercury stops expanding.
  3. The thermometer reading now equals your body temperature.
  4. This works because of the Zeroth Law: the thermometer (system C) mediates the comparison between your body and the temperature scale.
Maharashtra State Board: Class 11

Thermometric Property

A thermometric property is any physical property that changes measurably with temperature. The material exhibiting this property is called the thermometric substance.

Thermometric Property Thermometric Substance Thermometer Type
Volume of a liquid Mercury or Alcohol Liquid-in-glass thermometer
Electrical resistance of metal Platinum wire Resistance thermometer
Pressure of a gas Gas (at constant volume) Constant-volume gas thermometer
Electromotive force (EMF) Two dissimilar metals (e.g., Cu–Fe) Thermocouple
Resistance of a semiconductor Semiconductor material Thermistor
Maharashtra State Board: Class 11

Types of Thermometers

Thermometer Principle Range Strengths Limitations
Liquid-in-glass (Mercury) Volume expansion of a liquid −39 °C to 357 °C Simple, direct reading, portable Limited range, fragile, mercury is toxic
Liquid-in-glass (Alcohol) Volume expansion of a liquid −115 °C to 78 °C Good for low temperatures Short upper range, less precise
Constant Volume Gas Pressure of gas at fixed volume Very wide Most accurate, defines the temperature scale Bulky, slow to respond
Resistance (Platinum) Electrical resistance of metal −200 °C to 1200 °C Very accurate, wide range Bulky, best for steady temperatures
Thermocouple EMF between two dissimilar metal junctions Very wide Fast response, good for research Requires calibration
Thermistor Resistance of a semiconductor Limited Very sensitive, compact Non-linear response
Maharashtra State Board: Class 11

Characteristics of a Good Thermometer

A good thermometer must have these four qualities:

  1. Sensitivity — Detects small temperature changes
  2. Accuracy — Reads close to the true temperature
  3. Reproducibility — Gives the same reading under the same conditions
  4. Quick response — Reaches thermal equilibrium rapidly with the body being measured
Maharashtra State Board: Class 11

Example 1

Problem:
The average room temperature on a normal day is 27 °C. What is the room temperature in °F?
Solution:
Using Formula: TF = \[\frac{9}{5}\] × TC + 32
TF =\[\frac{9}{5}\] × 27 + 32
TF = 48.6 + 32
TF = 80.6 °F 
Maharashtra State Board: Class 11

Example 2

Problem:
Normal human body temperature is 98.6 °F. What is the body temperature in °C?
Solution:
Using Formula: TC = \[\frac{5}{9}\] × (TF - 32)
TC = \[\frac{5}{9}\] × (98.6 − 32) = \[\frac{5}{9}\] × 66.6
TC = 37 °C
Maharashtra State Board: Class 11

Example 3

Problem:
A mercury-in-glass thermometer has a column length of 25 mm at the ice point and 180 mm at the steam point. What is the temperature when the length is 60 mm?
Solution:
Using Formula: T = 100 × \[\frac{(P_T-P_1)}{(P_2-P_1)}\]
T = 100 × \[\frac {60−25}{180−25}\]
T = 100 × \[\frac {35}{155}\]
T = 22.58 °C
Maharashtra State Board: Class 11

Example 4

Problem:
A resistance thermometer has a resistance of 95.2 Ω at the ice point and 138.6 Ω at the steam point. What resistance corresponds to 27 °C?
Solution:
Using Formula rearranged: 27 = 100 × \[\frac {R−95.2}{138.6−95.2}\]
R = \[\frac {27×43.4}{100}\] + 95.2
R = 11.72 + 95.2
R = 106.92 Ω
Maharashtra State Board: Class 11

Summary

  1. Thermal equilibrium occurs when two bodies in contact reach the same temperature and heat flow stops.
  2. An adiabatic wall blocks heat; a diathermic wall allows it.
  3. The Zeroth Law of Thermodynamics: If A is in equilibrium with C, and B is in equilibrium with C, then A and B are in equilibrium — this is the scientific basis for thermometers.
  4. Three temperature scales: Celsius (common), Fahrenheit (USA), Kelvin (SI unit).
  5. Thermometric properties (volume, resistance, pressure, EMF) that change predictably with temperature are used to build thermometers.
  6. The constant-volume gas thermometer is the most accurate; liquid-in-glass thermometers are most common for everyday use.
  7. Thermocouples are used in research labs; thermistors in digital devices.

Test Yourself

Related QuestionsVIEW ALL [39]

Consider the following statements.
(A) The coefficient of linear expansion has dimension K–1.
(B) The coefficient of volume expansion has dimension K–1.

The steam point and the ice point of a mercury thermometer are marked as 80° and 20°. What will be the temperature on a centigrade mercury scale when this thermometer reads 32°?

A constant-volume thermometer registers a pressure of 1.500 × 104 Pa at the triple point of water and a pressure of 2.050 × 104 Pa at the normal boiling point. What is the temperature at the normal boiling point?

The temperatures of equal masses of three different liquids A, B and C are 12°C, 19°C and 28°C respectively. The temperature when A and B are mixed is 16°C, and when B and C are mixed, it is 23°C. What will be the temperature when A and C are mixed?

A metre scale made of steel reads accurately at 20°C. In a sensitive experiment, distances accurate up to 0.055 mm in 1 m are required. Find the range of temperature in which the experiment can be performed with this metre scale. Coefficient of linear expansion of steel  = 11 × 10–6 °C–1.

A circular disc made of iron is rotated about its axis at a constant velocity ω. Calculate the percentage change in the linear speed of a particle of the rim as the disc is slowly heated from 20°C to 50°C, keeping the angular velocity constant. Coefficient of linear expansion of iron = 1.2 × 10–5 °C–1.

An aluminium vessel of mass 0.5 kg contains 0.2 kg of water at 20°C. A block of iron of mass 0.2 kg at 100°C is gently put into the water. Find the equilibrium temperature of the mixture. Specific heat capacities of aluminium, iron and water are 910 J kg−1 K−1, 470 J kg−1 K−1 and 4200 J kg−1 K−1 respectively.

A copper cube of mass 200 g slides down on a rough inclined plane of inclination 37° at a constant speed. Assume that any loss in mechanical energy goes into the copper block as thermal energy. Find the increase in the temperature of the block as it slides down through 60 cm. Specific heat capacity of copper = 420 J kg−1 K−1.

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