🔥 Heat – Complete Chapter Notes

Introduction to Heat

Heat is a form of energy transferred between bodies or systems due to a temperature difference. It always flows from a region of higher temperature to lower temperature.

Main Features:

Measured in Joules (J); older unit: calorie (cal).
Different from temperature: Heat is energy in transit, temperature measures hotness/coldness.
Direction of heat flow: always from hot to cold.
Amount of heat (Q) depends on mass, temperature change, and nature of substance.

Basic Terms & Definitions

Heat (Q): Energy transferred due to temperature difference (Unit: joule, J).
Temperature (T): Degree of hotness or coldness (Unit: Kelvin, K; °C; °F).
Specific Heat Capacity (c): Heat needed to raise temperature of 1 kg of substance by 1K.
Q = m × c × ΔT
Thermal Expansion: Increase in size of body due to heating.
Latent Heat (L): Heat required to change state (solid–liquid or liquid–gas) without temperature change.
Q = m × L

1 calorie (cal) = 4.186 joule (J)

Modes of Heat Transfer

Conduction: Heat transfer through a solid by direct contact of particles (e.g., metal rod gets hot).
Convection: Transfer by movement of fluid (liquid or gas); e.g., hot air rising, sea breeze.
Radiation: Transfer by electromagnetic waves (no medium needed); e.g., heat from the Sun.

Mode	Medium Required?	Example
Conduction	Yes (solids)	Heating pan on stove
Convection	Yes (fluids)	Boiling water, sea breeze
Radiation	No	Solar heat, microwave oven

Conduction Formula:
Q = (k × A × ΔT × t) / l
where:
   Q = Heat transferred
   k = thermal conductivity
   A = area
   ΔT = temperature difference
   t = time
   l = length/thickness

Calorimetry & Principle of Mixtures

Calorimetry: Science of measuring heat exchange during physical and chemical changes.
Principle of Mixtures: In an isolated system, Heat lost = Heat gained.
m₁c₁(T₁−Tf) = m₂c₂(Tf−T₂)

Example: 100g water at 80°C is mixed with 100g water at 30°C.
Final temperature = (100×80 + 100×30)/(100+100) = 55°C

Thermal Expansion

Most substances expand when heated (solid, liquid, gas).
Linear Expansion: Increase in length
ΔL = α × L₀ × ΔT
Volumetric Expansion: Increase in volume
ΔV = β × V₀ × ΔT
Applications: Gaps in bridges, expansion joints on rails, thermometer capillaries.

Change of State & Latent Heat

Melting (Fusion): Solid → Liquid; Latent heat of fusion involved.
Boiling (Vaporisation): Liquid → Gas; Latent heat of vaporisation.
During phase change, temperature stays constant, heat is used to break bonds.

Heat for phase change:
Q = m × L

Example: How much heat to melt 250g of ice at 0°C? (L_fusion = 334 J/g)
Q = 250 × 334 = 83,500 J

Laws & Applications

Zeroth Law of Thermodynamics: If A is in thermal equilibrium with B, and B with C, then A is in equilibrium with C.
First Law: Energy supplied as heat = increase in internal energy + work done by system.
ΔQ = ΔU + ΔW
Applications: Refrigerator (heat pump), engine, human body temperature regulation, fire alarms.

Worked Examples & Numericals

Example 1: How much heat is needed to raise the temperature of 0.5 kg of water from 20°C to 70°C? (c=4200 J/kg·K)
Q = m × c × ΔT = 0.5 × 4200 × (70–20) = 0.5 × 4200 × 50 = 105,000 J
✅ Final Answer: 105,000 J

Example 2: An iron rod (length 1m, α=1.2×10⁻⁵/°C) is heated from 20°C to 120°C. Length increased by?
ΔL = α × L₀ × ΔT = 1.2×10⁻⁵ × 1 × (120–20) = 1.2×10⁻⁵ × 100 = 0.0012 m = 1.2 mm
✅ Final Answer: 1.2 mm

Example 3: 200g of water at 90°C is mixed with 100g at 30°C. Find final temperature.
Let x be final temp:
200×(90–x) = 100×(x–30) → 18000–200x = 100x–3000
→ 28000 = 300x → x ≈ 93.3°C (check for sensible results; usually solved as heat lost = heat gained)

Comprehensive Summary & Key Formulas

Heat always flows from hot to cold bodies.
Heat (Q) = m × c × ΔT
Phase change: Q = m × L
Expansion: ΔL = αL₀ΔT; ΔV = βV₀ΔT
Modes: Conduction, Convection, Radiation
Calorimetry: Heat lost = Heat gained
1 calorie = 4.186 J; Temperature units: °C, K, °F
First Law: ΔQ = ΔU + ΔW
Applications: Refrigerators, fire alarms, insulation, engines, thermos flasks