Heat & Thermodynamics

Heat is energy transferred between bodies due to a temperature difference. Temperature measures the average kinetic energy of molecules in a substance.

Temperature scales:

• Celsius (°C): water freezes at 0°C, boils at 100°C (at 1 atm).
• Fahrenheit (°F): freezes at 32°F, boils at 212°F.
• Kelvin (K): absolute scale, 0 K = −273.15°C (absolute zero, where molecular motion stops).

Conversions:

• °C to °F: F = (9/5)C + 32.
• °C to K: K = C + 273.
• 100°C = 212°F = 373 K. 0°C = 32°F = 273 K. −40°C = −40°F.

Specific heat capacity (c): heat needed to raise 1 kg of a substance by 1°C. Unit: J/kg·°C.

• Water: c = 4200 J/kg·°C (high — water heats and cools slowly, moderating climate).
• Aluminium: c ≈ 900 J/kg·°C.

Heat equation: Q = mcΔT (mass × specific heat × temperature change).

Latent heat: energy absorbed/released during phase change (no temperature change).

• Latent heat of fusion (melting ice → water) at 0°C: 334 kJ/kg.
• Latent heat of vaporization (water → steam) at 100°C: 2260 kJ/kg — large; that's why steam burns more than boiling water.

Modes of heat transfer:

1. Conduction — through solids by molecular collisions. Metals are good conductors. Cooking pans use metals.
2. Convection — by movement of fluid (liquid/gas). Hot water rises, cold sinks. Drives ocean currents and wind.
3. Radiation — by electromagnetic waves; no medium needed. The Sun's heat reaches Earth via radiation. Dark surfaces absorb more radiation than light ones.

Thermal expansion: most solids expand on heating. Gaps in railway tracks, expansion joints in bridges, mercury thermometers all rely on this. Water is anomalous — it expands between 4°C and 0°C (ice floats because ice is less dense than water).

Example 1 — Heat to warm water:
How much heat is required to raise 2 kg of water from 20°C to 80°C?
Method: Q = mcΔT = 2 × 4200 × 60 = 5,04,000 J = 504 kJ.

Example 2 — Mixing water:
500 g of water at 80°C is mixed with 500 g at 20°C. Final temperature?
Method: By symmetry (equal masses, same liquid): T_final = (80 + 20)/2 = 50°C. By energy conservation: 500×c×(80−T) = 500×c×(T−20) ⟹ T = 50°C.

Example 3 — Melting ice:
Heat required to melt 0.5 kg of ice at 0°C?
Method: Q = m × L_fusion = 0.5 × 334000 = 167,000 J = 167 kJ.

Example 4 — Temperature conversion:
What is 37°C in Fahrenheit?
Method: F = (9/5)×37 + 32 = 66.6 + 32 = 98.6°F — normal human body temperature.

Famous facts:

• Water has the highest specific heat capacity among common substances → useful as a coolant in cars and power stations.
• A pressure cooker raises the boiling point of water (~120°C at 2 atm) → faster cooking.
• Dew forms on cool nights because the ground radiates heat away and condenses moisture from cooler air.
• A vacuum flask (thermos) minimizes all three modes of heat transfer: vacuum stops conduction/convection, silvered walls reduce radiation.
• The temperature of the Sun's surface is ~5800 K; its core is ~15 million K.
• Liquid nitrogen boils at −196°C (77 K); liquid helium at −269°C (4 K).
• Mercury freezes at −39°C — that's why thermometers for very cold places use alcohol.

Trap: students confuse heat and temperature. A bucket of warm water has more heat than a candle flame, but the candle has a higher temperature. Heat depends on mass; temperature does not.