Heat & Thermodynamics – Part I

Topics covered: Temperature, Thermal Expansion, Calorimetry, Heat Transfer, Radiation, Laws of Cooling (JEE Main focus).

1. Temperature

• Temperature is a macroscopic physical quantity that measures the degree of hotness or coldness of a body.
• Heat naturally flows from higher temperature to lower temperature.
• Heat is the part of internal energy transferred due to temperature difference.
• Temperature is directly proportional to the average kinetic energy of random molecular motion.
• Two bodies are in thermal equilibrium when no heat flows between them.

Temperature scale relation:

(T_°C − 0) / 100 = (T_°F − 32) / 180 = (T_K − 273.15) / 100

2. Thermal Expansion

• Most substances expand on heating; some (like rubber) contract.
• Expansion is minimum in solids and maximum in gases.
• Solids show linear, areal, and volumetric expansion.

Linear Expansion

ΔL = α L ΔT

L_new = L (1 + αΔT)

Areal Expansion

ΔA = β A ΔT

A_new = A (1 + βΔT)

Volumetric Expansion

ΔV = γ V ΔT

V_new = V (1 + γΔT)

Relations: β = 2α, γ = 3α

Anomalous Expansion of Water

Water contracts on heating between 0°C and 4°C and expands above 4°C.

3. Specific Heat & Latent Heat

Specific heat capacity:

Q = mcΔT

Molar specific heat:

Q = nCΔT

Latent Heat:

• Fusion (Ice → Water): 80 cal/g
• Vaporisation (Water → Steam): 536 cal/g

4. Principle of Calorimetry

Heat lost = Heat gained

• Final temperature lies between the initial temperatures.
• Heat absorbed or released: Q = mcΔT
• During phase change: Q = mL

5. Heating Curve

• Sloping regions → temperature change
• Flat regions → phase change at constant temperature
• Slope ∝ 1 / specific heat

6. Heat Transfer

Conduction

Q = (KAΔTt) / L

Rate: dQ/dt = KA (dθ/dx)

Thermal Resistance:

• Series: R = R₁ + R₂ + …
• Parallel: 1/R = 1/R₁ + 1/R₂ + …

Convection

• Heat transfer by actual motion of fluid.
• Natural convection: density difference
• Forced convection: fan, pump, blower

7. Radiation

• No medium required.
• Fastest mode of heat transfer.
• Dark, rough surfaces are good absorbers.
• Shiny surfaces are good reflectors.

Black Body

• Absorbs all incident radiation.
• Emits radiation of all wavelengths.

Kirchhoff’s Law

Emissive power / Absorptive power = constant (at same temperature)

Stefan’s Law

R = σT⁴

Newton’s Law of Cooling

dT/dt ∝ (T − T₀)

Wien’s Displacement Law

λ_max T = 2.89 × 10⁻³ mK