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Physics · CDS

PC06 — Heat, Temperature & Thermodynamics

📖 PC06 · CDS General Science — Physics 🎯 CDS Level : High Priority

Heat and thermodynamics explain how energy flows between objects and how temperature, pressure, and volume of gases relate to each other. This chapter is tested every CDS cycle — especially temperature conversions, gas laws, modes of heat transfer, and the laws of thermodynamics.

📌 CDS tests in this chapter:
(1) Temperature conversions (°C ↔ °F ↔ K) and the unique reading where C = F;
(2) Modes of heat transfer — which mode works in vacuum;
(3) Latent heat — why boiling water stays at 100°C even with continued heating;
(4) Boyle's Law and Charles's Law — qualitative and basic numerical;
(5) First and Second Laws of thermodynamics — statement and implication;
(6) Good radiators/absorbers of heat — black body concept.

Topics at a Glance

① Heat vs Temperature

Definitions, scales, conversions

② Modes of Heat Transfer

Conduction, convection, radiation

③ Thermal Expansion

Linear, areal, cubical; bimetallic strip

④ Specific Heat & Latent Heat

Calorimetry; fusion; vaporisation

⑤ Laws of Thermodynamics

Zeroth, First, Second laws

⑥ Kinetic Theory & Gas Laws

Boyle's, Charles's, ideal gas equation

1. Heat vs Temperature & Temperature Scales

1.1

Defining Heat and Temperature

Two related but fundamentally different concepts

🔥 Heat (Q)

Form of energy in transit between bodies
Flows from higher to lower temperature
SI unit: Joule (J)
Old unit: Calorie (1 cal = 4.18 J)
Heat can change temperature OR state of matter

🌡️ Temperature

Degree of hotness or coldness of a body
Determines direction of heat flow
SI unit: Kelvin (K)
Common units: Celsius (°C), Fahrenheit (°F)
Temperature does NOT measure total heat energy

⚡ Temperature Scale Conversions

°C to °F: F = (9/5) × C + 32 °F to °C: C = (5/9) × (F − 32) °C to K: K = C + 273.15 (often written as 273) K to °C: C = K − 273 Special values: Absolute zero: 0 K = −273°C = −459.4°F Water freezes: 273 K = 0°C = 32°F Water boils: 373 K = 100°C = 212°F Body temperature: 310 K = 37°C = 98.6°F Equal C and F reading: −40° (both scales read −40)

The Kelvin scale starts at absolute zero — the lowest possible temperature where all molecular motion stops. Kelvin has no negative values.

Fig. 1 — Three temperature scales showing the same physical reference points. Kelvin never goes negative; absolute zero (0 K) is the lowest possible temperature.

2. Modes of Heat Transfer

2.1

Conduction, Convection & Radiation

Three distinct ways heat travels — each with different requirements

Fig. 2 — Conduction and convection require a medium (material); radiation does not — it travels through vacuum. This is why the Sun's heat reaches Earth through the vacuum of space.

📌 Good Conductors

Metals — especially silver, copper, aluminium
Used in cooking utensils (copper bottom)
Poor conductors: wood, rubber, glass — used as insulators
Air is a poor conductor — used in double-glazed windows

📌 Convection Examples

Sea breeze and land breeze (daily cycles)
Heating rooms — hot air rises, cool air sinks
Formation of clouds and thunderstorms
Oceanic currents; trade winds

📌 Radiation Facts

Black/dark surfaces: best absorbers AND radiators
Shiny/white surfaces: best reflectors, poor absorbers
Black body = perfect absorber (absorbs all radiation)
Thermos flask: vacuum + silver coating (reduces both conduction and radiation)

3. Thermal Expansion

3.1

How Matter Expands with Temperature

Most substances expand on heating and contract on cooling

⚡ Thermal Expansion Formulae

Linear expansion (length): ΔL = α L₀ ΔT (α = coefficient of linear expansion) Areal expansion (area): ΔA = β A₀ ΔT (β = 2α) Cubical expansion (volume): ΔV = γ V₀ ΔT (γ = 3α) Relationship: β = 2α and γ = 3α Example — Railway lines have gaps left between rails to allow for expansion in summer.

Exception — Water anomaly: Water contracts on cooling from 4°C to 0°C (unlike most liquids). Water has maximum density at 4°C. Below 4°C, water expands — this is why ice floats and why lakes freeze from the top down, protecting aquatic life.

💡 Bimetallic Strip: Two metals with different coefficients of expansion are bonded together. On heating, the metal with higher α expands more, causing the strip to bend toward the lower-α metal. Used in thermostats (electric irons, room heaters) and circuit breakers.

4. Specific Heat Capacity & Latent Heat

4.1

Heat Required to Change Temperature or State

Not all materials heat up equally — specific heat explains why

⚡ Specific Heat & Latent Heat

Heat absorbed/released to change temperature: Q = mcΔT m = mass (kg); c = specific heat capacity (J/kg·K); ΔT = temperature change Specific heat of water: c = 4200 J/kg·K (highest among common substances) Specific heat of iron: c ≈ 500 J/kg·K Specific heat of glass: c ≈ 670 J/kg·K Latent Heat (heat absorbed/released during change of state — at constant temp): Q = mL Latent heat of fusion of ice: L_f = 3.36 × 10⁵ J/kg Latent heat of vaporisation of water: L_v = 2.26 × 10⁶ J/kg Principle of Calorimetry: Heat lost by hot body = Heat gained by cold body m₁c₁(T₁−T_mix) = m₂c₂(T_mix−T₂)

Water has exceptionally high specific heat — it can absorb large amounts of heat with small temperature change. This makes it ideal as a coolant in engines and radiators, and explains why coastal areas have moderate climates compared to inland regions.

Fig. 3 — Heating curve of water. The flat portions at 0°C and 100°C represent phase changes where latent heat is absorbed without any rise in temperature. This is a direct CDS question concept.

📝 CDS PYQ

Heat & Temperature

Q1. At what temperature do the Celsius and Fahrenheit scales give the same reading?

(a) 0° (b) −40° (c) 100° (d) −100°

Answer: (b) −40°
Set °F = °C: C = (9/5)C + 32 → C − (9/5)C = 32 → (−4/5)C = 32 → C = −40. At −40°, both scales read the same value. This is a frequently repeated CDS and general science question. Remember: the answer is negative forty.

Q2. Which mode of heat transfer can occur through vacuum?

(a) Conduction only (b) Convection only (c) Radiation only (d) Conduction and convection

Answer: (c) Radiation only
Radiation travels as electromagnetic waves (infrared and visible light) and does not require any medium. It is the only mode that works in vacuum — this is how heat from the Sun reaches Earth across the vacuum of space. Conduction requires direct molecular contact; convection requires fluid movement — both need a material medium.

Q3. When water boils at 100°C and continues to be heated, what happens to its temperature?

(a) Increases beyond 100°C (b) Decreases (c) Remains at 100°C (d) Fluctuates

Answer: (c) Remains at 100°C
During a phase change (boiling or melting), all the heat supplied goes into breaking intermolecular bonds — none goes into raising the temperature. This energy is called latent heat of vaporisation. The temperature stays at 100°C until all the water has converted to steam. This is why the heating curve shows a flat line at 100°C.

Q4. Water is considered an excellent coolant because of its:

(a) Low boiling point (b) High specific heat capacity (c) Low density (d) High conductivity

Answer: (b) High specific heat capacity
Water's specific heat capacity (4200 J/kg·K) is among the highest of common substances. This means it can absorb a large amount of heat with only a small rise in temperature — ideal for carrying away heat from engines and radiators. The same property makes coastal regions milder (sea water moderates temperature swings) and causes sea breezes.

5. Laws of Thermodynamics

5.1

The Four Laws — Energy and Its Limits

These laws govern what is and is not possible in any energy transformation

Fig. 4 — The four laws of thermodynamics. CDS focuses on the First Law (ΔU = Q − W) and Second Law (heat flows hot to cold; no perfect engine).

6. Kinetic Theory & Gas Laws

6.1

Boyle's, Charles's & the Ideal Gas Equation

How pressure, volume, and temperature of a gas are mathematically linked

⚡ Gas Laws — Formulae

Boyle's Law (constant T): P₁V₁ = P₂V₂ Pressure and volume are inversely proportional at constant temperature. If pressure doubles → volume halves. Charles's Law (constant P): V₁/T₁ = V₂/T₂ Volume and temperature (in Kelvin) are directly proportional at constant pressure. If absolute temperature doubles → volume doubles. Gay-Lussac's Law (const V): P₁/T₁ = P₂/T₂ Pressure and temperature are directly proportional at constant volume. Ideal Gas Equation: PV = nRT P = pressure (Pa); V = volume (m³); n = number of moles R = 8.314 J/mol·K (universal gas constant); T = temperature in Kelvin At NTP (Normal Temp & Pressure): T = 273 K, P = 1 atm = 101,325 Pa 1 mole of ideal gas occupies 22.4 litres at NTP

Always use temperature in Kelvin in gas law calculations — never Celsius. Convert: K = °C + 273. Boyle's Law and Charles's Law are often directly tested with simple "what happens if pressure is doubled?" questions in CDS.

Fig. 5 — Boyle's Law: each curve (isotherm) shows P × V = constant. Higher temperature curves lie further from the origin. When pressure doubles, volume halves (and vice versa).

⚠ CDS Gas Law Trap: Charles's Law requires temperature in Kelvin. If a gas at 27°C has its temperature doubled, the new temperature is NOT 54°C — it is 600 K (=54 + 273... wait: 27°C = 300 K; doubling gives 600 K = 327°C). Always convert Celsius to Kelvin before applying Charles's Law.

📝 CDS PYQ

Thermodynamics & Gas Laws

Q1. A gas at constant temperature has its pressure doubled. What happens to its volume?

(a) Doubles (b) Becomes four times (c) Halves (d) Remains the same

Answer: (c) Halves
By Boyle's Law: P₁V₁ = P₂V₂ at constant temperature. If P₂ = 2P₁, then 2P₁V₂ = P₁V₁ → V₂ = V₁/2. Volume halves. This is the most directly tested gas law question in CDS. Pressure and volume are inversely proportional at constant temperature.

Q2. The first law of thermodynamics is essentially a statement of:

(a) Newton's third law (b) Conservation of momentum (c) Conservation of energy (d) Second law of motion

Answer: (c) Conservation of energy
The First Law of Thermodynamics states: ΔU = Q − W (internal energy change = heat added minus work done by system). This is simply the law of conservation of energy applied to thermodynamic systems — energy is neither created nor destroyed, only converted between heat, work, and internal energy.

Q3. Which surface is the best radiator of heat?

(a) White polished surface (b) Rough black surface (c) Red coloured surface (d) Shiny silver surface

Answer: (b) Rough black surface
A rough black (matt black) surface is both the best absorber and the best emitter/radiator of heat radiation. A shiny or white surface is a poor absorber (reflects most radiation) and therefore also a poor emitter. This is why cooking pots are often dark on the outside (emit heat from food efficiently) and why thermos flasks are silvered inside (to reduce radiation).

📚 Formula Sheet — PC06

🌡️ Temperature

°F = (9/5)°C + 32
K = °C + 273
C = F at −40°
Absolute zero = 0 K = −273°C
Water: 0°C=273K, 100°C=373K

🔥 Heat & Thermal Expansion

Q = mcΔT (temperature change)
Q = mL (phase change, latent heat)
ΔL = αL₀ΔT; ΔV = 3αV₀ΔT
c_water = 4200 J/kg·K (highest)
Max density of water at 4°C

⚡ Gas Laws

P₁V₁ = P₂V₂ (Boyle's, const T)
V₁/T₁ = V₂/T₂ (Charles's, const P)
P₁/T₁ = P₂/T₂ (const V)
PV = nRT (ideal gas)
1 mole ideal gas = 22.4 L at NTP

📦 Thermodynamics

1st Law: ΔU = Q − W
2nd Law: heat flows hot → cold
No engine converts all heat to work
Black body = perfect absorber & radiator
Radiation only mode working in vacuum

⚡ Quick Revision Booster — PC06

🌡️ Scale Facts

K = °C + 273 (add 273)
°F = (9/5)°C + 32
C = F only at −40°
Boiling: 100°C / 212°F / 373 K
Absolute zero: 0 K / −273°C

🔥 Heat Transfer

Conduction: solids (metals best)
Convection: fluids only
Radiation: works in vacuum
Black = best absorber AND radiator
Thermos: vacuum + silver coating

💧 Special Water Facts

Max density at 4°C (not 0°C)
c = 4200 J/kg·K (very high)
L_fusion = 3.36 × 10⁵ J/kg
L_vaporisation = 2.26 × 10⁶ J/kg
Ice floats — density less than water

☁ Gas Laws

Boyle: P doubles → V halves
Charles: always use Kelvin!
PV = nRT (ideal gas)
Real gases: high P / low T → deviate
STP: 0°C / NTP: 25°C (sometimes)

☄ Thermodynamics

1st Law: energy is conserved
2nd Law: entropy increases
No perfect heat engine (efficiency < 100%)
Carnot engine = maximum efficiency
Refrigerator: work extracts heat from cold

🚨 CDS Traps

Latent heat: temp stays constant during phase change
Radiation: not affected by medium
Heat and temperature: different concepts
Charles's Law: use K, not °C
Water is densest at 4°C, not 0°C

📝 Practice Exercise

Attempt these before checking the answers below.

E-01

What is 37°C expressed in Fahrenheit?

(a) 99.6°F
(b) 98.6°F
(c) 100°F
(d) 96°F

E-02

A gas has volume 6 litres at pressure 2 atm. At constant temperature, if pressure becomes 3 atm, new volume is:

(a) 9 L
(b) 3 L
(c) 4 L
(d) 12 L

E-03

Thermal expansion of a liquid is measured by which coefficient?

(a) α (linear)
(b) β (areal)
(c) γ (cubical)
(d) κ (compressibility)

E-04

Which statement about the Second Law of Thermodynamics is correct?

(a) Energy is conserved in all processes
(b) Heat spontaneously flows from cold to hot
(c) No heat engine can be 100% efficient
(d) Entropy always decreases in natural processes

E-05

Equal masses of water and iron are given the same amount of heat. Water has a higher specific heat. Which one shows a greater temperature rise?

(a) Water
(b) Iron
(c) Both rise equally
(d) Depends on initial temperature

Answers: E-01: (b) 98.6°F [F = (9/5)×37 + 32 = 66.6 + 32 = 98.6] | E-02: (c) 4 L [P₁V₁ = P₂V₂ → 2×6 = 3×V₂ → V₂ = 4 L] | E-03: (c) γ (cubical — liquids occupy volume, not just length or area) | E-04: (c) No heat engine can be 100% efficient — some heat is always wasted (entropy increases) | E-05: (b) Iron — higher specific heat means more heat needed per °C rise; iron (lower c) rises more for same heat input

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