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Heat (Q)
Energy that is transferred from one object to another because of a temperature difference.
Temperature
A measure of the average kinetic energy of the molecules in a substance.
Internal Energy (U)
The total microscopic energy of all molecules in a system; for an ideal gas it depends only on temperature.
Joule (J)
The SI unit of energy and heat.
calorie (cal)
Amount of heat required to raise the temperature of 1 g of water by 1 °C; 1 cal = 4.186 J.
Calorie (kcal)
Food calorie; equals 1 kcal = 1000 cal = 4186 J.
Ideal Gas
A gas whose molecules do not interact except through elastic collisions and obey PV = nRT.
Boltzmann Constant (k_B)
Relates average translational kinetic energy of particles to temperature; k_B ≈ 1.38 × 10⁻²³ J/K.
Universal Gas Constant (R)
R = 8.314 J/mol·K; links macroscopic and microscopic gas properties.
Degrees of Freedom
Independent ways a molecule can store energy (e.g., three translational directions for monoatomic gases).
Monoatomic Gas Internal Energy
U = (3/2) nRT or (3/2) Nk_B T, arising solely from translational motion.
Diatomic Gas Internal Energy
U = (5/2) nRT at ordinary temperatures (three translational + two rotational modes).
Specific Heat Capacity (c)
Heat required to raise the temperature of 1 kg of a substance by 1 K (or 1 °C).
Heat–Temperature Equation
Q = mcΔT, linking heat added/removed to mass, specific heat, and temperature change.
Units of Specific Heat
J/kg·K or J/kg·°C.
Specific Heat at Constant Volume (c_v)
Heat required to raise 1 kg of gas by 1 K when volume is held constant (no PV work).
Specific Heat at Constant Pressure (c_p)
Heat required to raise 1 kg of gas by 1 K while pressure stays constant (includes PV work).
Relation between cp and cv
For an ideal gas, cp = cv + R.
Calorimetry
Science of measuring heat exchange in physical or chemical processes using energy conservation.
Closed System
Exchanges energy but not mass with its surroundings.
Open System
Can exchange both mass and energy with its environment.
Isolated System
Exchanges neither mass nor energy with surroundings; ΣQ = 0 within the system.
Calorimeter
Insulated apparatus used to measure heat transfer, typically with water as the absorbing medium.
Bomb Calorimeter
Sealed, high-pressure calorimeter used to measure heat released during combustion (food energy determination).
Latent Heat (L)
Energy absorbed or released during a phase change at constant temperature; Q = ±mL.
Heat of Fusion (L_F)
Latent heat needed to melt 1 kg of a solid at its melting point (water: 334 kJ/kg).
Heat of Vaporization (L_V)
Latent heat needed to vaporize 1 kg of a liquid at its boiling point (water: 2.26 MJ/kg).
Sign Convention for Q
Q > 0 when heat is absorbed (endothermic); Q < 0 when heat is released (exothermic).
Conduction
Heat transfer through direct molecular collisions within a material.
Fourier’s Law of Conduction
Rate: Q/t = kA(ΔT)/d, where k is thermal conductivity, A area, d thickness.
Thermal Conductivity (k)
Material property indicating how well a substance conducts heat (units W/m·°C).
Convection
Heat transfer by bulk movement of a fluid (liquid or gas).
Natural Convection
Fluid motion driven by density differences from heating (e.g., warm air rising).
Forced Convection
Fluid motion produced by external means (fan, pump, heart) to enhance heat transfer.
Radiation
Heat transfer via electromagnetic waves; requires no medium.
Stefan-Boltzmann Law
Radiative heat rate: Q/t = εσAT⁴, with σ = 5.67×10⁻⁸ W/m²·K⁴.
Emissivity (ε)
Dimensionless measure (0–1) of how effectively a surface emits/absorbs radiation.
Net Radiative Heat Transfer
Q/t = εσA(T₁⁴ − T₂⁴) between an object (T₁) and surroundings (T₂).
Good Absorber = Good Emitter
Surfaces that absorb radiation well (dark, matte) also emit efficiently; shiny surfaces do both poorly.
Sea Breeze
Example of natural convection where cooler sea air replaces rising warm air over land.
Insulation
Use of low-k materials (e.g., fiberglass, Styrofoam) to reduce heat transfer.