Unit 10 · Heat Capacity and Modes of Heat Transfer · Athens Academy

Heat Capacity and Modes of Heat Transfer

Unit 10 is the thermal physics backbone of Class 10. Every question in this chapter connects to one core idea — heat moves from hot to cold, and how it moves depends on the medium. FBISE tests definitions, numericals, diagrams, and real-life applications every year. Master this unit and you master a guaranteed 15–20 marks.

1 · Heat Capacity and Specific Heat

Heat capacity

★ Definition — Heat Capacity (examinable)
Heat capacity of a body is the amount of heat energy required to raise its temperature by 1 °C (or 1 K).
Symbol: C Formula: C = Q / ΔT SI Unit: J K^-1

Where Q = heat supplied (J) and ΔT = rise in temperature (K).

Specific heat capacity

★ Definition — Specific Heat Capacity (examinable)
Specific heat capacity of a material is the amount of heat energy required to raise the temperature of 1 kg of the substance by 1 K (or 1 °C).
Symbol: c Formula: c = Q / (m ΔT) SI Unit: J kg^-1 K^-1

Q = m c ΔT (rearranged form — the one used in every numerical)

Symbols: Q = heat (J); m = mass (kg); ΔT = T_final − T_initial = temperature change (K or °C — same numerical value for a change).

🧠 Memory aid — “Quick Camel Drinks Tea” → Q · m · c · ΔT. Every time you write Q = m c ΔT, say those four words and you will never forget the order.

Important: The size of 1 °C and 1 K is the same. So ΔT in °C equals ΔT in K. Only the starting number differs (25 °C = 298 K, but a rise of 50 °C = a rise of 50 K).

Specific heats of common substances (FBISE Table)

Substance	c (J kg^-1 K^-1)	Substance	c (J kg^-1 K^-1)
Water	4 190	Iron / Steel	452
Ethanol	2 450	Copper	387
Glycerine	2 410	Silver	235
Aluminium	910	Gold	129
Glass	840	Lead	128

Key point: Water has by far the largest specific heat (4 190). Metals like copper and lead have very low values — they heat up and cool down quickly.

High vs low specific heat — comparison

Property	HIGH specific heat (e.g. water)	LOW specific heat (e.g. metals)
Heating speed	Heats up slowly	Heats up quickly
Cooling speed	Cools down slowly	Cools down quickly
Heat storage	Retains heat for a long time	Cannot retain heat for long
Typical use	Coolant / temperature buffer	Heat sinks, cooking utensils
Example	Water, ethanol, glycerine	Iron, copper, aluminium

Five uses of water’s large specific heat ★ (past-paper favourite)

A. Temperature variation — land vs coast. Dry soil has specific heat ≈ 800 J kg^-1 K^-1, roughly 5× smaller than water. Inland cities like Multan or Lahore swing from 5 °C (winter) to 48 °C (summer). Coastal Karachi stays between 19 °C and 32 °C because the Arabian Sea acts as a temperature buffer.

B. Ocean and lake stability. Large water bodies heat and cool slowly, keeping temperature stable and providing a safe habitat for aquatic life.

C. Body temperature regulation. The human body is ≈ 60% water. This large specific heat lets the body absorb or release heat without a sudden change — keeping us near 37 °C.

D. Cooling systems. Water carries away large amounts of heat from car radiators and industrial heat exchangers without itself getting too hot.

E. Cooking. Water heats slowly and distributes heat evenly — curries cook without burning, and hot drinks stay warm longer.

🧠 Memory aid — T-O-B-C-C: Temperature variation, Ocean stability, Body, Cooling system, Cooking. Say “To Be Cool Calm Cook.”

2 · Three Modes of Heat Transfer

★ Definition — Heat Transfer (examinable)
Heat transfer is the movement of thermal energy from one object to another due to a difference in temperature. It continues until both reach thermal equilibrium.

Mode	Medium / state	Mechanism
Conduction	Solids (mainly metals)	Atom-to-atom vibration + flow of free electrons
Convection	Liquids and gases	Bulk motion of fluid due to density difference
Radiation	No medium needed — even vacuum	Travels as infrared (electromagnetic) waves at speed of light

3 · Conduction

★ Definition — Conduction (examinable)
Conduction is the transfer of heat due to collisions of atoms or molecules and the motion of free electrons, in solids, from the hot part to the cold part.

Mechanism — 5 steps

Step 1	One end of a metal rod is heated.
Step 2	Atoms at the hot end gain energy and vibrate with larger amplitude.
Step 3	These vibrating atoms collide with neighbours and pass on energy.
Step 4	In metals, free electrons travel from hot to cold end, carrying energy rapidly.
Step 5	Heat is progressively transferred along the rod from hot to cold end.

Key result: Metals are good conductors because they have many free electrons. Non-metals (wood, glass, rubber) lack free electrons — they are poor conductors (good insulators).

Conduction — atoms vibrate and collide; free electrons carry energy from hot to cold end.

Experiment — good vs bad conductors

Three rods of copper, aluminium and iron of equal length are fitted with wax pins at their far ends. When heated equally at one end, the copper pin falls first, then aluminium, then iron — confirming Cu > Al > Fe in conductivity.

🧠 Memory aid — “Copper Always Ignites Brass last” → Copper, Aluminium, Iron, Brass — fastest to slowest conductor.

⚠️ Common error — “A metal spoon feels colder than a wooden spoon — so metal must be colder.” Both are at room temperature. Metal conducts heat away from your hand faster, making it feel colder.

4 · Convection

★ Definition — Convection (examinable)
Convection is the transfer of heat due to the bulk movement of molecules in fluids (liquids and gases). It cannot take place in solids.

Mechanism — 4 steps

Step 1	Fluid at the bottom is heated; it expands and becomes less dense.
Step 2	The less-dense hot fluid rises upward.
Step 3	Cooler, denser fluid from above sinks to take its place.
Step 4	This continuous cycle forms a convection current that distributes heat throughout the fluid.

🧠 Memory aid — “Hot Up · Cold Down.” Hot fluid rises (less dense), cold fluid sinks (more dense). That is convection in four words.

Sea breeze (daytime)

During the day, land heats up faster than the sea (land has lower specific heat). Air above the land becomes hot, expands, and rises. Cool air from the sea moves in to replace it — this is the sea breeze.

Sea breeze — land heats faster; hot air rises; cool sea air flows in to replace it.

Land breeze (nighttime)

At night, land cools faster than the sea (water retains heat longer). Air above the sea is now warmer and rises; cool air from the land moves toward the sea — this is the land breeze.

⚠️ Common error — Students reverse the directions. Remember: the breeze is named after where it comes FROM. Sea breeze comes from the sea. Land breeze comes from the land.

Thermals and bird flight

The sun heats dark/concrete surfaces more than grass or water. Air above these hot patches becomes less dense and rises — forming a column of warm rising air called a thermal. Eagles, hawks and vultures spread their wings, circle inside thermals to gain altitude, then glide between thermals to travel great distances using almost no energy.

5 · Radiation

★ Definition — Radiation (examinable)
Radiation is the transfer of heat in the form of electromagnetic waves (mainly infrared). It does not require any medium and can travel through vacuum.

Key facts: radiation travels at the speed of light (3 × 10⁸ m s^-1); every object emits and absorbs infrared radiation; hotter objects emit far more. This is how the Sun’s heat crosses 150 million km of vacuum to reach Earth.

Four factors affecting radiation

Factor	More radiation when…	Example
Surface colour	Surface is matt black	Solar panels; laptop charger vents
Surface texture	Surface is rough and dull	Radiator fins vs polished kettle
Surface area	Area is larger	Radiator fins increase area to lose heat faster
Temperature	Object is hotter	Sun (5 500 °C) vs human body (37 °C)

Surface	Absorbing	Emitting	Reflecting
Matt black	Best ✓✓	Best ✓✓	Worst ✗
White	Bad ✗	Bad ✗	Good ✓
Shiny silver	Worst ✗✗	Worst ✗✗	Best ✓✓

🧠 Memory aid — “Black Beats Best · Silver Saves.” Black = Best at absorbing and emitting. Silver = Saves (reflects) heat best.

⚠️ Common error — “Black is a good absorber but a bad emitter.” This is wrong. A good absorber is also a good emitter. Matt black is best at both.

The Leslie cube experiment

A hollow metal cube with four different surfaces (matt black, dull dark, white, shiny silver) is filled with hot water — so all faces are at the same temperature. An IR thermometer measures radiation from each face. The matt-black face emits the most; shiny silver emits the least.

6 · Applications of Heat Transfer

Cooking pan — all three modes

Conduction: heat conducts from the flame through the metal base to the food. The handle is wood or plastic (insulators) to stay cool.
Convection: water near the bottom heats up, rises; cooler water sinks — cooking food evenly.
Radiation: the flame and hot pan radiate infrared heat to the surroundings.

Thermos (vacuum) flask

A thermos flask blocks all three modes:

Vacuum gap	Blocks conduction (no medium) and convection (no fluid).
Silvered walls	Reflect radiation back — very low emissivity.
Plastic stopper	Blocks heat loss through the top (poor conductor).
Insulating base	Stops conduction through the bottom.

Building insulation

Double-glazed windows (two glass panes with trapped air or vacuum) block conduction and convection. Foam in walls and false ceilings traps air. White-painted exteriors in Pakistan reflect sunlight to keep homes cooler.

Infrared thermometers

An IR thermometer detects infrared radiation emitted by an object and converts it to a temperature reading — without touching the object. Used in medical screening (COVID-19), industrial furnaces, and hazardous environments. Each device has a Distance-to-Spot (D:S) ratio — e.g. 12:1 means at 12 inches it reads a 1-inch spot.

7 · Greenhouse Effect and Global Warming

★ Definition — Greenhouse Effect (examinable)
The greenhouse effect is the process through which heat is trapped near Earth’s surface by greenhouse gases (water vapour, carbon dioxide, methane, nitrogen oxide).

★ Definition — Global Warming (examinable)
Global warming is the long-term increase in the average temperature of Earth’s atmosphere and oceans, primarily due to human activities (burning fossil fuels) since the pre-industrial period (1850–1900).

Mechanism — 5 steps

Step 1	Short-wavelength solar radiation passes through the atmosphere and is absorbed by Earth’s surface.
Step 2	Earth’s surface warms up and re-emits energy as long-wavelength infrared radiation.
Step 3	Greenhouse gases (CO₂, CH₄, H₂O vapour) absorb this outgoing IR.
Step 4	Greenhouse gases re-emit the IR back toward Earth.
Step 5	Earth stays warm enough for life. Without this, night temperatures would drop to ≈ −180 °C.

Six effects of global warming ★

Effect	Cause	Pakistan connection
Flooding	Glacier melt raises sea levels	2022 floods — one-third of Pakistan submerged
Hurricanes	Warmer oceans fuel stronger storms	Arabian Sea cyclones intensifying
Heavier rainfall	More evaporation → more moisture	Extreme monsoon seasons
Droughts	Greater evaporation dries soil	Balochistan water scarcity
Wildfires	Drier vegetation burns more easily	KPK forest fires
Winter storms	More atmospheric moisture → heavier snow	Murree January 2022 tragedy

🧠 Memory aid — F-H-R-D-W-W: Flooding, Hurricanes, Rainfall, Droughts, Wildfires, Winter storms. Say “Floods Hurt Regions Daily — Worldwide Warming.”

8 · Geothermal Activity

Layer	State	Temperature	Composition
Inner core	Solid (high pressure)	≈ 6 000 °C	Iron and nickel
Outer core	Liquid (molten)	≈ 4 000 °C	Molten iron and nickel
Mantle	Semi-solid (plastic)	1 000–3 500 °C	Silicate rocks
Crust	Solid	Cold at surface	Thin outer shell (5–70 km)

Why Earth’s core stays hot — four reasons

A. Residual heat	Primordial heat from Earth’s formation 4.5 billion years ago is still stored in the core.
B. Radioactive decay	Uranium-238, thorium-232 and potassium-40 continuously release heat as they decay.
C. Gravitational compression	Gravity compresses the core, raising its pressure and temperature.
D. Crust as insulator	The thick crust prevents heat escaping rapidly — it insulates the core.

9 · Worked Examples

Example 1 · Finding specific heat from heat data

Given: m = 200 g = 0.2 kg; T_initial = 25 °C; T_final = 75 °C; Q = 3 500 J.

ΔT = 75 − 25 = 50 K. Using c = Q / (m ΔT) = 3 500 / (0.2 × 50) = 3 500 / 10.

∴ c = 350 J kg^-1 K^-1

⚠️ Common error — Plugging in 75 instead of ΔT = 50. Always subtract initial from final.

Example 2 · Heat absorbed by aluminium

Given: m = 0.5 kg; c = 900 J kg^-1 K^-1; T_initial = 25 °C; T_final = 100 °C.

ΔT = 75 K. Q = 0.5 × 900 × 75 = 33 750 J.

∴ Q = 33 750 J = 33.75 kJ

⚠️ Common error — Mixing up subtraction order. Always do FINAL minus INITIAL for ΔT.

Example 3 · Mixture method ★ (find specific heat of a solid)

Given: Solid m_s = 150 g, heated to 100 °C, dropped into 200 g water at 25 °C in a 50 g calorimeter (c_c = 0.9 J g^-1 °C^-1). Final temperature = 30 °C. c_w = 4.18 J g^-1 °C^-1.

Heat lost = Heat gained: m_s c_s (100 − 30) = (m_w c_w + m_c c_c)(30 − 25)

150 × c_s × 70 = (836 + 45) × 5 = 4 405 → c_s = 4 405 / 10 500

∴ c_s = 0.42 J g^-1 °C^-1

⚠️ Common error — Forgetting the calorimeter’s heat gain. Always write two terms on the gained side — water + calorimeter. This is the #1 mark-losing mistake in mixture questions.

Example 4 · Unit conversion (most-missed)

Given: m = 500 g of water; c = 4 200 J kg^-1 K^-1; T_initial = 20 °C; T_final = 70 °C.

Convert: m = 0.5 kg. ΔT = 50 K. Q = 0.5 × 4 200 × 50 = 105 000 J.

∴ Q = 105 000 J = 105 kJ

⚠️ Common error — Using 500 g directly. Specific heat is in J kg^-1 K^-1 — always convert grams → kg before substituting.

10 · Common Mistakes

✗ Wrong — what students write	✓ Correct — what the examiner expects
“Conduction occurs in liquids and gases.”	Conduction occurs mainly in solids (especially metals).
“Convection takes place in all three states.”	Convection takes place only in fluids. NOT in solids.
“Radiation needs a medium to travel.”	Radiation does NOT need a medium — it travels through vacuum.
“Sea breeze blows from land to sea during the day.”	Sea breeze blows from sea to land. Named after where it comes FROM.
“Black is a good absorber but a bad emitter.”	A good absorber is also a good emitter. Matt black is best at both.
Q = m c T (no Δ)	Q = m c ΔT — the Δ means CHANGE in temperature, not the final value.

11 · Short Questions (Section A)

Q1 · Define specific heat capacity. Write its formula and SI unit. [3 marks]

Specific heat capacity is the amount of heat energy required to raise the temperature of 1 kg of a substance by 1 K (or 1 °C). [1] Formula: c = Q / (m ΔT). [1] SI unit: J kg^-1 K^-1. [1]

Q2 · Why is water used as a coolant in car radiators? [3 marks] ★

Water has a very large specific heat capacity (4 190 J kg^-1 K^-1). [1] This allows it to absorb a large amount of heat from the engine without its own temperature rising too much. [1] This prevents engine overheating, making water an ideal coolant. [1]

Q3 · Distinguish between conduction and convection (any three points). [3 marks]

(i) Conduction occurs in solids; convection occurs in fluids. [1] (ii) In conduction, particles vibrate in fixed positions; in convection, particles physically move. [1] (iii) Conduction does not involve bulk motion; convection does. [1]

Q4 · Why does a metal door handle feel colder than the wooden part, although both are at room temperature? [3 marks] ★

Metals are good conductors of heat; wood is a poor conductor. [1] The metal rapidly conducts heat away from your hand. [1] The wooden part does not conduct heat away as fast, so the metal feels colder even though both are at the same temperature. [1]

Q5 · Why do crowded city areas feel hotter than outskirts on a hot summer day? [3 marks]

Cities have dark concrete and asphalt with low specific heat — they absorb sunlight quickly and re-emit IR radiation. [1] Outskirts have grass, trees and water (higher specific heat, shade). [1] Dense buildings also block wind, trapping heat — the urban heat-island effect. [1]

12 · Last-Minute Exam Checklist

✓ Have you written the SI unit on every numerical answer (J kg^-1 K^-1 for c; J for Q)?
✓ Have you used ΔT (change in temperature), not T_final, in Q = m c ΔT?
✓ Have you converted grams → kg before substituting into any SI formula?
✓ Do you know the FBISE definitions word-for-word — Specific Heat, Conduction, Convection, Radiation, Greenhouse Effect, Global Warming?
✓ Can you draw a clearly labelled sea breeze AND land breeze diagram with the correct wind direction?
✓ Do you know the Leslie cube result: matt black = best emitter and absorber; shiny silver = best reflector?
✓ Can you list the four factors affecting radiation: Colour, Texture, Area, Temperature?
✓ Can you explain the greenhouse effect in 5 steps with a labelled diagram?
✓ Do you know all six effects of global warming (F-H-R-D-W-W) with Pakistani examples?
✓ Can you name the four reasons Earth’s core stays hot: residual heat, radioactive decay, gravitational compression, crust insulation?
✓ In mixture problems, have you included both water and calorimeter on the heat-gained side?
✓ Have you described the thermos flask blocking all three modes: vacuum, silvered walls, plastic stopper?

If you have studied this chapter carefully, you have already mastered what most students skip. Heat Capacity and Modes of Heat Transfer is the examiner’s guaranteed unit — and now it is yours too. Write the definitions, draw the diagrams, show every step of your working. Walk into that exam hall knowing that heat is just energy on the move — and you are ready to move with it.

🔬 Chapter 10 · Heat Capacity and Modes of Heat Transfer