Chapter 3 — Thermal Physics: Long Answer Questions
Boyle's Law (1662)
Statement: At constant temperature, the volume of a fixed mass of gas is inversely proportional to its pressure.
Mathematical form:
Graphical representation:
- P vs V: rectangular hyperbola
- P vs 1/V: straight line through origin
Example: If a gas occupies 4 L at 1 atm pressure, at 2 atm pressure its volume = (1 × 4)/2 = 2 L
Explanation at molecular level: If volume decreases, the same number of molecules occupy less space → they collide with the walls more frequently → pressure increases.
Charles' Law (1787)
Statement: At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature (in Kelvin).
Mathematical form:
Temperature must be in Kelvin: T(K) = T(°C) + 273
Example: A gas occupies 2 L at 300 K. At 600 K (same pressure): V₂ = V₁ × T₂/T₁ = 2 × 600/300 = 4 L
Combined Gas Law
Combining Boyle's Law and Charles' Law:
This holds when only the quantity of gas is fixed (mass constant).
Ideal Gas Law (including amount of gas):
Where n = number of moles, R = universal gas constant = 8.314 J/mol·K
1. Conduction
Definition: Transfer of heat through a medium by direct contact between particles, without any net movement of the medium itself.
Mechanism: Vibrating molecules in the hotter part collide with adjacent molecules, transferring kinetic energy from molecule to molecule in a chain.
Characteristics:
- Occurs mainly in solids (liquids and gases are poor conductors)
- No movement of medium
- Heat flows from hot end to cold end
Rate of conduction (Fourier's Law): Q/t = kA(ΔT/L)
Where k = thermal conductivity, A = cross-sectional area, ΔT = temperature difference, L = length
Examples:
- Metal rod becomes hot when one end is placed in fire
- Cooking in metal pans
- Ice cubes cool a drink through the glass
Good conductors: Copper, aluminium, silver (metals — free electrons help) Poor conductors (insulators): Wood, rubber, glass, wool, air
2. Convection
Definition: Transfer of heat through fluids (liquids and gases) by the actual movement of heated matter (convection currents).
Mechanism: Heated fluid becomes less dense and rises; cooler, denser fluid sinks to take its place → circular convection currents form.
Types:
- Natural (free) convection: Driven by density differences due to temperature (no external force)
- Forced convection: Fan or pump forces fluid movement
Examples:
- Sea breeze and land breeze (atmospheric convection)
- Boiling water (heated water at bottom rises; cooler water at top sinks)
- Radiators warm a room by convection
- Ventilation in buildings
- Oceanic currents
3. Radiation
Definition: Transfer of heat in the form of electromagnetic waves (infrared radiation) without any medium.
Characteristics:
- Does NOT require a medium — occurs in vacuum
- Travels at the speed of light (3 × 10⁸ m/s)
- All objects above absolute zero emit radiation
- Hotter objects emit more radiation
Examples:
- Heat from the Sun reaching Earth through vacuum of space
- Feeling warmth near a bonfire without touching it
- Thermal imaging cameras detect infrared radiation
- Greenhouse effect — Earth's surface radiates heat; atmosphere re-radiates it back
Black body: An ideal body that absorbs all radiation falling on it and emits maximum radiation (best emitter and best absorber). Dull, black surfaces are good emitters and absorbers; shiny, white surfaces are poor emitters and poor absorbers.
Specific Heat Capacity
Definition: The amount of heat energy required to raise the temperature of 1 kg of a substance by 1°C (or 1 K).
Symbol: s or c Unit: J/(kg·K) or J/(kg·°C)
Where:
- Q = heat energy absorbed or released (J)
- m = mass of substance (kg)
- s = specific heat capacity (J/kg·K)
- ΔT = change in temperature = T_final − T_initial (K or °C)
Values of specific heat capacity:
| Substance | s (J/kg·K) |
|---|---|
| Water | 4200 |
| Ethanol | 2400 |
| Aluminium | 900 |
| Iron | 450 |
| Copper | 385 |
| Lead | 128 |
Water's high specific heat capacity makes it ideal for cooling systems and explains why coastal areas have milder climates.
Principle of Calorimetry (Principle of Mixtures)
Statement: When two bodies at different temperatures are mixed and reach thermal equilibrium, the heat lost by the hotter body = heat gained by the cooler body (assuming no heat loss to surroundings).
Where T₁ > T_mix > T₂
A calorimeter is an insulated container used to measure heat exchange.
Worked Problem: 200 g of water at 80°C is mixed with 300 g of water at 20°C. Find the final temperature. (s of water = 4200 J/kg·K)
Heat lost by hot water = Heat gained by cold water m₁s(T₁ − T) = m₂s(T − T₂) 0.2 × 4200 × (80 − T) = 0.3 × 4200 × (T − 20)
Since s cancels: 0.2(80 − T) = 0.3(T − 20) 16 − 0.2T = 0.3T − 6 22 = 0.5T T = 44°C
Where:
- Q = heat energy (J)
- m = mass (kg)
- L = specific latent heat (J/kg)
Latent Heat of Fusion (L_f)
Definition: The heat energy required to convert 1 kg of a solid to liquid at its melting point (or released when liquid solidifies), without change in temperature.
For ice: L_f = 3.34 × 10⁵ J/kg = 334 J/g
Example: To melt 500 g of ice at 0°C: Q = mL = 0.5 × 3.34 × 10⁵ = 1.67 × 10⁵ J
Why ice cools drinks so effectively: Ice absorbs 334 J/g as latent heat as it melts, before the meltwater heats up. Compare: to heat 1 g of water from 0°C to 100°C requires only 100 × 4.2 = 420 J. The latent heat is nearly equal — so ice cools a drink by absorbing much more heat than just warming cold water would.
Latent Heat of Vaporisation (L_v)
Definition: The heat energy required to convert 1 kg of liquid to vapour at its boiling point (or released when vapour condenses), without change in temperature.
For water: L_v = 2.26 × 10⁶ J/kg = 2260 J/g
Example: To vaporise 200 g of water at 100°C: Q = mL = 0.2 × 2.26 × 10⁶ = 4.52 × 10⁵ J
Why steam burns are more severe than boiling water burns: Steam at 100°C releases 2260 J/g as it condenses on skin (latent heat), THEN releases additional heat as the resulting hot water cools. Boiling water only releases heat as it cools from 100°C.
Biological significance: Sweating uses latent heat of vaporisation of water — 1 g of sweat evaporating removes 2260 J from the body, efficiently cooling it.
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