Thermometer A and B have ice point marked at 15° and 25° and steam points a 75° and 125° respectively. When thermo-meter A measures the temperature of a bath as 60°, the reading of B for the same bath is

1. Basics of Heat and Temperature (basic)

To master thermal physics, we must first distinguish between two terms often used interchangeably in daily life: Heat and Temperature. At the molecular level, every substance is composed of particles in constant motion. Heat represents the total kinetic energy resulting from this molecular movement. In contrast, Temperature is a measure of the average kinetic energy of those particles—it is essentially a gauge of how 'hot' or 'cold' an object is in degrees FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI, Solar Radiation, Heat Balance and Temperature, p.70. Think of heat as the total energy contained in a system, while temperature is the intensity of that energy.

How does heat behave? It follows the second law of thermodynamics, naturally flowing from a body of higher temperature to one of lower temperature. This transfer continues through processes like conduction—where heat moves through direct contact—until both bodies reach thermal equilibrium (the same temperature) FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI, Solar Radiation, Heat Balance and Temperature, p.68. Interestingly, adding heat doesn't always raise the temperature. During a phase change (like ice melting into water), the temperature remains constant. This is because the energy supplied—known as latent heat—is being used to break the molecular bonds rather than increasing the particles' speed Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.295.

To quantify temperature, we use scales defined by fixed points, typically the Ice Point (where pure water freezes) and the Steam Point (where it boils). Because the expansion of materials (like mercury) is generally linear, we can create a relationship between any two temperature scales using the following fundamental ratio:

(Reading - Ice Point) / (Steam Point - Ice Point) = Constant

This formula ensures that regardless of the units used—Celsius, Fahrenheit, or a custom scale—the relative position of a temperature reading remains the same across all systems.

Feature	Heat	Temperature
Definition	Total energy of molecular motion.	Measure of hotness or coldness.
SI Unit	Joule (J)	Kelvin (K)
Work Potential	Can perform work directly.	Indicates direction of heat flow.

Sources: FUNDAMENTALS OF PHYSICAL GEOGRAPHY, Geography Class XI, Solar Radiation, Heat Balance and Temperature, p.68, 70; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.295

2. Standard Temperature Scales: Celsius, Kelvin, and Fahrenheit (basic)

To measure how hot or cold an object is, we need a standard reference. This is where temperature scales come in. Most thermometers work on the principle that substances like mercury expand when heated and contract when cooled GC Leong, Weather, p.117. To create a scale, scientists use two "fixed points": the Ice Point (where pure water freezes) and the Steam Point (where pure water boils at standard atmospheric pressure).

There are three primary scales you must master for any scientific discussion on thermal physics:

• Celsius (°C): Formerly called Centigrade, this is the most common scale used globally for weather and scientific work. It sets the ice point at 0°C and the steam point at 100°C, dividing the range into 100 equal parts NCERT Class VII, Understanding the Weather, p.31.
• Fahrenheit (°F): Often used in clinical thermometers and in the US, it sets the ice point at 32°F and the steam point at 212°F. This creates a range of 180 units between freezing and boiling GC Leong, Weather, p.117.
• Kelvin (K): Known as the Absolute Scale, it is the SI unit of temperature. It starts at Absolute Zero (0 K), the theoretical point where all molecular motion stops. Note that we don't use the "degree" symbol (°) for Kelvin.

While these scales look different, they all measure the same physical reality. We can convert between them using a simple principle of linear calibration. The ratio of the current reading minus the ice point over the total range (steam point minus ice point) is always constant for any linear scale:

(Reading - Ice Point) / (Steam Point - Ice Point) = Constant

Using this, we derive the standard conversion formula: C/5 = (F - 32)/9 = (K - 273)/5. For instance, a common summer temperature in India like 45°C NCERT Class IX, Climate, p.30 would be roughly 113°F.

Feature	Celsius	Fahrenheit	Kelvin
Ice Point	0°C	32°F	273.15 K
Steam Point	100°C	212°F	373.15 K
Intervals	100 units	180 units	100 units

Sources: Certificate Physical and Human Geography, GC Leong, Weather, p.117; Exploring Society: India and Beyond, NCERT Class VII, Understanding the Weather, p.31; Contemporary India-I, NCERT Class IX, Climate, p.30

3. Principles of Thermometry and Expansion (intermediate)

At the heart of thermometry lies the principle of thermal expansion: the tendency of matter to change its shape, area, and volume in response to a change in temperature. For a substance to be used in a thermometer, it must possess a thermometric property—a physical quality that varies linearly and predictably with heat. In common laboratory thermometers, this property is the volume of a liquid. We often use Mercury because it is the only metal that remains liquid at room temperature and possesses a very uniform rate of expansion Science, Class VIII, Nature of Matter, p.123. Alternatively, Alcohol (Ethanol) is used for measuring lower temperatures because its freezing point is significantly lower than that of water, though it is highly volatile Science, Class X, Carbon and its Compounds, p.72.

To create a functional scale, we must establish Fixed Points. These are reproducible temperatures, typically the Ice Point (melting point of pure ice) and the Steam Point (boiling point of water at standard pressure). Once these points are marked on a thermometer, the distance between them is divided into equal intervals called degrees. Whether you are using a Celsius, Fahrenheit, or a completely custom scale, the fundamental logic remains the same: the proportion of the current reading relative to the total range is constant across all linear scales.

Feature	Mercury Thermometer	Alcohol Thermometer
Working Liquid	Mercury (Liquid Metal)	Ethanol (often dyed red)
Advantage	Does not stick to glass; high boiling point.	Low freezing point; safer for domestic use.
Range Suitability	High-temperature industrial/lab use.	Very cold climates or weather monitoring.

Mathematically, we use the Linear Calibration Formula to convert between scales. For any two thermometers, A and B, the relationship is expressed as:

(Reading - Ice Point) / (Steam Point - Ice Point) = Constant

This constant represents the fraction of the total expansion the liquid has undergone. If a thermometer has a range of 100 units and is at the halfway mark, it will read 50; if another scale has a range of 60 units, its halfway mark will read 30 (plus its specific ice point offset). This consistency allows scientists to calibrate new instruments against known standards.

Sources: Science, Class VIII, Nature of Matter: Elements, Compounds, and Mixtures, p.123; Science, Class X, Carbon and its Compounds, p.72

4. Heat Transfer and Thermal Equilibrium (intermediate)

At its core, heat transfer is the movement of thermal energy from a region of higher temperature to one of lower temperature. This process continues until the two regions reach the same temperature, a state known as thermal equilibrium. Think of it like water flowing between two connected tanks; it will only stop moving once the levels are equal. In thermal physics, when objects are in equilibrium, there is no net exchange of heat between them.

Nature employs three distinct mechanisms to move this energy, often occurring simultaneously in our environment Science-Class VII . NCERT(Revised ed 2025), Heat Transfer in Nature, p.97:

Mechanism	Medium Required	Key Characteristic
Conduction	Solid (mostly)	Transfer through direct contact between molecules without bulk movement of the material.
Convection	Fluids (Liquids/Gases)	Transfer through the actual movement of the heated matter (convection currents).
Radiation	None (Vacuum/Air)	Transfer via electromagnetic waves; does not require a medium to travel Science-Class VII . NCERT(Revised ed 2025), Heat Transfer in Nature, p.102.

To measure these changes, we use thermometers calibrated between two fixed points: the Ice Point (where water freezes) and the Steam Point (where water boils). Because the expansion of the material inside a thermometer is typically linear, any temperature scale can be related to another using the principle of linear interpolation. The ratio of the current reading relative to the total range (Steam Point - Ice Point) remains constant across different scales. This is why we can convert Celsius to Fahrenheit or any custom scale by simply comparing how far the "reading" has traveled from the ice point relative to the full scale distance Science Class VIII . NCERT(Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.143.

An interesting phenomenon occurs during a phase change (like ice melting into water). Even though we continue to supply heat, the temperature of the substance remains constant until the phase change is complete Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.295. This energy, known as latent heat, is used to break the molecular bonds rather than increasing the kinetic energy (temperature) of the particles.

Sources: Science-Class VII . NCERT(Revised ed 2025), Heat Transfer in Nature, p.97; Science-Class VII . NCERT(Revised ed 2025), Heat Transfer in Nature, p.102; Science Class VIII . NCERT(Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.143; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.295

5. Specific Heat and Phase Changes (intermediate)

In thermal physics, we distinguish between heat that changes temperature and heat that changes state. The first concept is Specific Heat. This is the amount of heat energy required to raise the temperature of a unit mass of a substance by 1°C. Water is a thermal outlier because it has an exceptionally high specific heat—about 2.5 times higher than landmass Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.286. This means water acts as a massive heat reservoir; it requires significantly more energy to warm up and takes much longer to cool down compared to rocks or soil. This explains why the Southern Hemisphere, which is dominated by oceans, remains cooler and why coastal regions experience moderate climates with low diurnal temperature ranges Physical Geography by PMF IAS, Tropical Cyclones, p.369.

The second core concept is Phase Change and Latent Heat. When a substance reaches its melting or boiling point, a curious phenomenon occurs: the temperature stops rising even though you continue to add heat. This "hidden" energy is called Latent Heat Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.294. Instead of increasing the kinetic energy (temperature) of the molecules, this energy is used to break the intermolecular bonds holding the substance in its current state (solid or liquid). For instance, while ice melts, the mixture of ice and water remains at 0°C until every crystal has turned to liquid Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.294.

Process	Type of Latent Heat	Energy Action
Melting (Solid → Liquid)	Latent Heat of Fusion	Absorbed
Evaporation (Liquid → Gas)	Latent Heat of Vaporization	Absorbed
Condensation (Gas → Liquid)	Latent Heat of Condensation	Released

This cycle is vital for Earth's energy balance. Water evaporates from oceans by absorbing latent heat, and when that vapor later condenses into clouds in the atmosphere, it releases that stored energy as Latent Heat of Condensation Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.295. This release of energy is the primary engine that fuels powerful weather systems like tropical cyclones.

Sources: Physical Geography by PMF IAS, Horizontal Distribution of Temperature, p.286; Physical Geography by PMF IAS, Tropical Cyclones, p.369; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.294; Physical Geography by PMF IAS, Vertical Distribution of Temperature, p.295

6. General Formula for Temperature Scale Conversion (exam-level)

To master temperature conversions, we must understand that most thermometers operate on the principle of linear expansion. Whether it is a clinical thermometer used in medicine or a laboratory thermometer used in science Exploring Society: India and Beyond, Understanding the Weather, p.31, the scale is calibrated between two universally recognized "fixed points": the Lower Fixed Point (LFP), representing the ice point, and the Upper Fixed Point (UFP), representing the steam point.

The core principle is that the proportionate position of a temperature reading between these two points remains constant across any linear scale. We express this universal relationship with the General Formula for Scale Conversion:

(Reading - LFP) / (UFP - LFP) = Constant

This "constant" value represents the fraction of the total range that the current temperature occupies. For instance, in the Centigrade (Celsius) scale, the freezing point of water is 0°C and the boiling point is 100°C Certificate Physical and Human Geography, Weather, p.117. In the Fahrenheit scale, these points are 32°F and 212°F respectively. By setting their conversion ratios equal to each other, we can derive the standard conversion formulas used in geography and physics.

Temperature Scale	Lower Fixed Point (LFP)	Upper Fixed Point (UFP)	Fundamental Interval (UFP - LFP)
Celsius (°C)	0°C	100°C	100 units
Fahrenheit (°F)	32°F	212°F	180 units
Custom Scale (X)	Ice Point of X	Steam Point of X	Total divisions on X

This formula is incredibly powerful because it allows you to convert between any two scales, even "faulty" thermometers or custom scales used in specific scientific instruments, simply by knowing their respective ice and steam points.

Sources: Exploring Society: India and Beyond, Understanding the Weather, p.31; Certificate Physical and Human Geography, Weather, p.117

7. Solving the Original PYQ (exam-level)

To solve this, you must apply the fundamental concept of linear interpolation between two fixed points—the ice point and the steam point. As you've learned in your conceptual modules, while different thermometers use different numerical scales, the ratio of the current reading's position relative to the total range remains constant across all linear scales. By using the universal formula (Reading - Ice Point) / (Steam Point - Ice Point) = Constant, you are essentially determining what fraction of the way the temperature has traveled from freezing to boiling.

Walking through the logic, for thermometer A, the reading of 60° sits 45 units above the ice point (60 - 15) within a total range of 60 units (75 - 15). This simplifies to a 3/4 or 75% position on the scale. To find the equivalent on thermometer B, you apply this same 75% proportion to its 100-unit range (125 - 25). Since 75% of 100 is 75, you simply add this value to thermometer B's starting ice point (25 + 75), leading you directly to the correct answer (D) 100°. Always remember to add the ice point back at the end; forgetting this step is a frequent source of error in competitive exams, as noted in principles found in NCERT Physics Class XI.

UPSC often includes distractors like (A) 60° to catch students who assume the scales are identical without checking the ranges, or (B) 75° for those who correctly calculate the interval but forget to add the starting offset of 25°. Option (C) 90° is a common trap for those who might make a quick mental calculation error regarding the ratio. Success in these General Science questions depends on your ability to look past the specific numbers and recognize the underlying physical proportionality.