CDS Physics · Heat and Thermodynamics

Temperature and Heat Transfer

How the Kelvin, Celsius and Fahrenheit scales are linked, the three ways heat moves (conduction, convection and radiation), and the calorimetry rule that heat lost equals heat gained.

All Heat and Thermodynamics notes

Why this matters

Eight CDS questions from 2018 (I) to 2026 (I). Three ask for the formula linking two temperature scales, four ask how heat moves in an everyday case, and one names the principle behind heat lost = heat gained.

Concept 1 of 3: Temperature scales: Kelvin, Celsius and Fahrenheit

A temperature scale needs two fixed points. Celsius puts melting ice at 0 and boiling water at 100. Fahrenheit puts the same two points at 32 and 212, so 100 Celsius degrees cover 180 Fahrenheit degrees. Kelvin uses the Celsius degree but starts counting from absolute zero, the coldest possible temperature, which is 273.15 degrees below 0 °C.

Definition

The three scales and how to move between them:

Kelvin from Celsius: add 273.15 (often rounded to 273). A Kelvin degree and a Celsius degree are the same size.
Absolute zero is 0 K, which is $-273.15$ °C. Nothing can be colder.
Fahrenheit from Celsius: multiply by $\tfrac{9}{5}$ , then add 32. The 9/5 comes from 180 F degrees for every 100 C degrees; the 32 is the ice point on the Fahrenheit scale.
Celsius from Fahrenheit: subtract 32, then multiply by $\tfrac{5}{9}$ .
The Celsius and Fahrenheit readings are equal at $-40$ .

Converting between temperature scales

T = t_C + 273.15 \qquad T_F = \tfrac{9}{5}\,T_C + 32 \qquad T_C = \tfrac{5}{9}\,(T_F - 32)

Ttemperature in kelvin
$t_C,\ T_C$ temperature in degrees Celsius
$T_F$ temperature in degrees Fahrenheit

Worked example

A cup of tea is at 50 °C. Write this temperature in kelvin and in degrees Fahrenheit.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2023 · CDS (II) 2023 — General Knowledge · Q37Easy

Example 1 · Heat and Thermodynamics · Temperature and Heat Transfer

Which one of the following is the correct relation between Celsius and Fahrenheit temperature scales ? (Symbols carry their usual meanings)

Add 273 to go from Celsius to Kelvin, never subtract

The Kelvin number is always the bigger one, because the Kelvin scale starts lower, at absolute zero. So

T = t_C + 273

. A relation such as

T = t_C - 273

T = 273 - t_C

gives a negative Kelvin reading for a warm day, which is impossible.

The Fahrenheit constant is 32, and the factor is 9/5

Ice melts at 32 °F, so the constant added is 32, not 36. Each Celsius degree is 9/5 of a Fahrenheit degree, so the factor is 9/5, not 5/9 or 10/3. Check any formula with one point: 100 °C must give 212 °F.

Drill 2 more on temperature scales: kelvin, celsius and fahrenheit

Concept 2 of 3: Conduction, convection and radiation

Heat always flows from hot to cold, and it has three ways to travel. In conduction, heat passes from particle to particle while the material stays where it is, as along a metal spoon. In convection, the warm fluid itself moves and carries the heat with it, as in a pot of boiling water. In radiation, heat travels as waves and needs no material at all, which is how the Sun warms the Earth across empty space.

Definition

The three modes and their tests:

Conduction: heat passes through a material without the material moving. Best in metals, because of their free electrons. Copper conducts better than aluminium.
Convection: a heated fluid becomes lighter and rises, cooler fluid sinks in its place, and the moving fluid carries the heat. Happens only in liquids and gases.
Radiation: heat travels as electromagnetic waves (mostly infrared). Needs no medium, so it crosses a vacuum.
Poor conductors: liquids are poor, gases are poorer. Even hydrogen, the best conducting gas, conducts far less than water.
Cooling quickly: water carries heat away from a hot bowl much faster than air, and moving air (a fan) removes the warm, moist layer so the water keeps cooling by evaporation.

Everyday case	Main mode of heat transfer
Heating one end of a brass rod warms the other end	Conduction
Water boiling in a pot on a gas stove	ConvectionQ CDS 2024 (II): boiling water in a pot is the example of convection.
Land and sea breezes	Convection
Warm air circulating round a blast furnace	Convection
Feeling the warmth of the Sun	Radiation
Glass of an electric bulb heated by the glowing filament	RadiationQ CDS 2018 (II): this is the one case in a list that is not convection.
Thermal conductivity, highest to lowest	Copper, aluminium, water, hydrogen gasQ CDS 2026 (I): hydrogen gas has the least thermal conductivity of these four.
Cooling a hot bowl of rice fast	Stand it in water and run a fan at full speedQ CDS 2024 (I): a water bath with a fast fan beats still air, a cooled room or water alone.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2024 · CDS (II) 2024 — General Knowledge · Q22Easy

Example 2 · Heat and Thermodynamics · Temperature and Heat Transfer

Which one of the following heat transfers is an example of convection ?

A microwave oven does not heat by convection

The microwaves are absorbed by the water in the food, which heats the food from within. That is heating by radiation absorbed in the food, not by moving hot air. Convection needs a fluid that flows and carries the heat.

Every gas is a poor conductor, even the best one

Hydrogen conducts heat better than any other gas, but every gas conducts far less than water, and water far less than a metal. A question asking for the least conductor among metals, water and a gas wants the gas.

Radiation needs no medium; conduction and convection do

The Sun's heat crosses empty space, so it must be radiation. Conduction needs a material to pass through, and convection needs a fluid that can flow.

Drill 3 more on conduction, convection and radiation

Concept 3 of 3: Specific heat and the principle of calorimetry

Put a hot body and a cold body together, with no heat escaping, and heat flows from the hot one to the cold one until both are at the same temperature. No heat is made or lost, so all the heat the hot body gives out is taken in by the cold body. This is the principle of calorimetry. How much heat a body takes for each degree depends on its mass and on its material, through a number called the specific heat.

Definition

Heat and temperature change:

Heat taken in or given out: $Q = mc\,\Delta T$ , where $c$ is the specific heat of the material.
Specific heat is the heat needed to raise 1 kg of a substance by 1 K. Its SI unit is J kg⁻¹ K⁻¹.
Water has a very high specific heat, about 4200 J kg⁻¹ K⁻¹, so it is used as a coolant in car radiators.
Principle of calorimetry: in an isolated mixture, heat lost by the hot body = heat gained by the cold body. It is the law of conservation of energy applied to heat.
Thermal equilibrium is the end state of that exchange: both bodies at one common temperature.

Heat for a temperature change, and the calorimetry balance

Q = m\,c\,\Delta T \qquad m_1 c_1 (T_1 - T) = m_2 c_2 (T - T_2)

Qheat taken in or given out, in joules
mmass, in kg
cspecific heat of the material
$\Delta T$ change in temperature
Tthe common final temperature of the mixture

Worked example

200 g of water at 80 °C is mixed with 300 g of water at 20 °C. No heat escapes. Find the final temperature of the mixture.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

CDS · 2018 · CDS (I) 2018 — General Knowledge · Q32Easy

Example 3 · Heat and Thermodynamics · Temperature and Heat Transfer

Which of the following represents a relation for 'heat lost = heat gained'?

Calorimetry and thermal equilibrium are not the same name

Heat lost = heat gained is the principle of calorimetry. Thermal equilibrium is only the final state, when the two temperatures have become equal. A question asking for the relation 'heat lost = heat gained' wants calorimetry.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Temperature scales: Kelvin, Celsius and Fahrenheit
Converting between temperature scales
$T = t_C + 273.15 \qquad T_F = \tfrac{9}{5}\,T_C + 32 \qquad T_C = \tfrac{5}{9}\,(T_F - 32)$
Specific heat and the principle of calorimetry
Heat for a temperature change, and the calorimetry balance
$Q = m\,c\,\Delta T \qquad m_1 c_1 (T_1 - T) = m_2 c_2 (T - T_2)$

Reference tables (1)

Conduction, convection and radiation8 rows

Everyday case	Main mode of heat transfer
Heating one end of a brass rod warms the other end	Conduction
Water boiling in a pot on a gas stove	ConvectionQ CDS 2024 (II): boiling water in a pot is the example of convection.
Land and sea breezes	Convection
Warm air circulating round a blast furnace	Convection
Feeling the warmth of the Sun	Radiation
Glass of an electric bulb heated by the glowing filament	RadiationQ CDS 2018 (II): this is the one case in a list that is not convection.
Thermal conductivity, highest to lowest	Copper, aluminium, water, hydrogen gasQ CDS 2026 (I): hydrogen gas has the least thermal conductivity of these four.
Cooling a hot bowl of rice fast	Stand it in water and run a fan at full speedQ CDS 2024 (I): a water bath with a fast fan beats still air, a cooled room or water alone.

Watch out for (6)

Add 273 to go from Celsius to Kelvin, never subtract
→ Temperature scales: Kelvin, Celsius and Fahrenheit
The Fahrenheit constant is 32, and the factor is 9/5
→ Temperature scales: Kelvin, Celsius and Fahrenheit
A microwave oven does not heat by convection
→ Conduction, convection and radiation
Every gas is a poor conductor, even the best one
→ Conduction, convection and radiation
Radiation needs no medium; conduction and convection do
→ Conduction, convection and radiation
Calorimetry and thermal equilibrium are not the same name
→ Specific heat and the principle of calorimetry

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