Chapter 8: Formula Reference — Heat and Thermodynamics

Celsius to Fahrenheit

F = (9/5)C + 32

Fahrenheit to Celsius

C = (5/9)(F − 32)

Celsius to Kelvin

K = C + 273.15

Kelvin to Celsius

C = K − 273.15

Fixed points (Celsius)

Ice point = 0°C, Steam point = 100°C

Fixed points (Fahrenheit)

Ice point = 32°F, Steam point = 212°F

Absolute zero

0 K = −273.15°C (theoretical lowest possible temperature)

Heat energy (temperature change)

Q = mcΔT

Q = heat (J), m = mass (kg), c = specific heat capacity (J/kg·K), ΔT = temperature change (K)

Heat energy (phase change, latent heat)

Q = mL

L = latent heat (J/kg): Lf for fusion (melting), Lv for vaporisation

Principle of Calorimetry

Heat lost by hot body = Heat gained by cold body

Assuming no heat loss to surroundings

Specific latent heat of fusion of ice

Lf = 3.34 × 10⁵ J/kg

Standard value at 0°C

Specific latent heat of vaporisation of water

Lv = 22.6 × 10⁵ J/kg

Standard value at 100°C

Linear expansion

L = L₀(1 + αΔT)

α = coefficient of linear expansion (K⁻¹)

Areal (superficial) expansion

A = A₀(1 + βΔT)

β = coefficient of areal expansion (K⁻¹), β ≈ 2α

Cubical (volume) expansion

V = V₀(1 + γΔT)

γ = coefficient of cubical expansion (K⁻¹), γ ≈ 3α

Boyle's Law

PV = constant (at constant T)

P = pressure (Pa), V = volume (m³)

Charles's Law

V/T = constant (at constant P)

T = absolute temperature (K)

Gay-Lussac's Law

P/T = constant (at constant V)

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Ideal Gas Equation

PV = nRT

n = number of moles, R = universal gas constant = 8.314 J/(mol·K)

Combined Gas Law

P₁V₁/T₁ = P₂V₂/T₂

For a fixed mass of gas across two states

Zeroth Law of Thermodynamics

If two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other

Basis for the concept and measurement of temperature

First Law of Thermodynamics

ΔQ = ΔU + ΔW

ΔQ = heat supplied, ΔU = change in internal energy, ΔW = work done by the system; a statement of energy conservation

Second Law of Thermodynamics

Heat cannot spontaneously flow from a colder to a hotter body without external work; entropy of an isolated system never decreases

Governs the direction of natural processes

Third Law of Thermodynamics

The entropy of a perfect crystal approaches zero as temperature approaches absolute zero

Absolute zero is unattainable in practice

Efficiency of a heat engine

η = W/Q₁ = 1 − Q₂/Q₁

Q₁ = heat absorbed, Q₂ = heat rejected, W = net work done

Carnot Engine Efficiency

η = 1 − T₂/T₁

T₁ = source temperature, T₂ = sink temperature (both in kelvin); maximum possible efficiency between two temperatures

Conduction

Q/t = kAΔT/d

k = thermal conductivity (W/m·K), A = cross-sectional area, d = thickness, ΔT = temperature difference across the material

Convection

Heat transferred by actual movement of fluid particles

Occurs in liquids and gases

Radiation (Stefan–Boltzmann Law)

E = σT⁴

E = energy radiated per unit area per unit time, σ = Stefan-Boltzmann constant = 5.67 × 10⁻⁸ W/(m²·K⁴), T = absolute temperature

Wien's Displacement Law

λmaxT = constant (b = 2.898 × 10⁻³ m·K)

λmax = wavelength of peak emission; relates temperature of a body to the wavelength at which it radiates most strongly