Physics #1 - Heat

Heat (Thermal Energy)

Thermal energy in transfer. Symbol: Q. SI unit: joule (J). CGS unit: calorie (cal).

Calorie Conversion to Joules

1 cal ≈ 4.2 J

Temperature

Measure of how hot or cold an object is. Symbol: T. SI unit: kelvin (K). Other units: °C / °F.

Mass (m)

Quantity of matter in an object. SI unit: kilogram (kg); frequently used: grams (g).

Specific Heat Capacity (c or s)

Heat needed to raise 1 kg of a substance by 1 K. SI unit: J/(kg·K). CGS unit: cal/(g·°C).

Heat Capacity (C)

Heat needed to raise the whole object by 1 K. SI unit: J/K.

Latent Heat (L)

Heat required to change state of a substance at constant temperature. SI unit: J/kg.

Latent Heat of Fusion

Heat required for solid to liquid phase change. Value: 80 cal/g.

Latent Heat of Vaporization

Heat required for liquid ↔ gas phase change. Value: 540 cal/g (2260 J/g).

Definition of Calorie

Amount of heat needed to change the temperature of 1g of water from 14.5°C to 15.5°C.

Formula: Temperature Change (No Phase Change)

Q = mcΔT (Used for heating/cooling solids, liquids, or gases staying in the same state).

Formula: Heat Capacity Problem + is used when

Q = CΔT (Used when an object is given by its heat capacity C instead of mass and specific heat).

Formula: Phase Change

Q = mL (Used for melting/freezing or boiling/condensing at constant temperature).

Water Equivalent

Mass of water that absorbs or releases the exact same amount of heat as a given object for the same temperature change.

Specific Heat of Water (Liquid)

1 cal/g°C or 4.184 J/g°C

Specific Heat of Ice

0.48 cal/g°C or 2.01 J/g·°C

Specific Heat of Steam

0.48 cal/g°C or 2.01 J/g·°C

Specific Heat of Aluminum

0.21 cal/g°C or 0.90 J/g·°C

Specific Heat of Iron

0.11 cal/g°C or 0.45 J/g·°C

Heat vs. Temperature

Heat is total transferred energy (depends on mass); temperature is a measure of hotness/coldness (independent of mass).

Reason for Thermal Expansion (Atomic Theory)

Heating increases atomic vibration amplitude; asymmetric potential energy curve increases average interatomic distance.

Expansion of Isotropic Materials

Expands like a photographic enlargement; a cavity inside an isotropic body expands just like the material itself.

Thermal Stress

Stress developed when a rigidly fixed rod is subjected to a temperature change, causing compressive or tensile forces.

Anomalous Behavior of Water

Between 0°C and 4°C, water contracts on heating and expands on cooling (behavior normalizes above 4°C).

Consequences of Water's Anomalous Behavior

Lakes freeze from the top down, 4°C water sinks (maximum density), and aquatic life survives at the bottom.

Applications of Thermal Expansion

Gaps in railway tracks, slack transmission cables, pyrex labware, and thermal shrinking of iron rims onto cartwheels.

Sublimation

Direct conversion of a solid into a vapour state (e.g., NH4Cl, camphor).

Condensation

Conversion of matter from a gaseous or vapour state back into a liquid state.

Evaporation vs. Boiling

Evaporation occurs slowly at any temperature only at the surface; boiling occurs rapidly throughout the liquid at a specific boiling point.

Triple Point of Water

Temperature: 0.01°C, Pressure: 0.006 atm (611.65 Pa), where solid, liquid, and vapor coexist in equilibrium.

Critical Point of Water

Temperature: 374°C, Pressure: 221 atm, above which liquid and vapor become indistinguishable (supercritical fluid).

Conduction

Heat transfer from particle to particle without overall dislocation of particles; dominant in solids. Direction: T1 > T2.

Variable State vs. Steady State in Conduction

In variable state, temperature changes with time; in steady state, temperature at each point becomes constant and heat flow is uniform.

Conduction Formula (Fourier's Law)

Q/t = KA(T1 - T2) / L, where K is thermal conductivity, A is area, and L is length.

Thermal Conductivity (K) Order

Silver > Copper > Aluminium > Iron (Ag > Cu > Al > Fe).

Thermal Resistance Formula

R = L / (KA), representing opposition to heat flow through a material.

Kirchhoff's Junction Law (Thermal/Electrical)

The algebraic sum of all currents meeting at a node (or junction) is zero; incoming equals outgoing current.

Growth of Ice on Lake

Time taken to increase ice thickness is proportional to the square of the thickness (t proportional to x²).

Convection

Heat transfer via actual movement of a heated fluid (liquid or gas). Divided into natural (density-driven) and forced (pump/fan-driven).

Thermal Radiation

Heat transfer that requires no material medium, travels in straight lines, and obeys the inverse square law.

Reflection, Absorption, and Transmission (RAT)

Incident radiation divides into reflected (r), absorbed (a), and transmitted (t) fractions, where r + a + t = 1.

Prevost's Theory of Heat Exchange

At every temperature except 0 K, a body continuously exchanges heat energy with its surroundings.

Ideal Black Body

An ideal object that absorbs all radiation hitting it, reflecting nothing. Emitted radiation depends only on its temperature.

Stefan-Boltzmann Law

Radiant energy emitted per unit area per second is proportional to the fourth power of absolute temperature: E = σT^4.

Factors Affecting Rate of Cooling

Emissivity (e), surface area, mass, specific heat, and temperature difference relative to surroundings.

Wein's Displacement Law

The peak wavelength of radiation emitted by a blackbody is inversely proportional to its absolute temperature: λ_m * T = b.

Color-Temperature Relation in Radiation

Higher temperature shifts peak emission to shorter wavelengths (violet end); lower temperature shifts it to longer wavelengths (red end).