Thermal Physics (Unit 04) - Study Guide

Core Definitions:

• • Thermal Equilibrium: State in which there is no net flow of thermal energy between two objects in thermal contact.
• • Zeroth Law of Thermodynamics: If two thermodynamic systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other.
• • Coefficient of Linear Expansion (α): The fractional increase in length per unit rise in temperature.

Equations:

• • Kelvin Temperature: T = θ + 273.15 (T: Kelvin, θ: Celsius)
• • Linear Expansion: Δl = l₀ αΔθ
• • Area Expansion: ΔA = A₀ βΔθ (β = 2α)
• • Volume Expansion: ΔV = V₀ γΔθ (γ = 3α)
• • Real liquid expansion: γ_real = γ_app + γ_vessel (Real expansion = Apparent expansion + Vessel expansion)

Key Points:

• • The constant volume gas thermometer is considered the standard reference thermometer.
• • Anomalous expansion of water occurs between 0°C and 4°C. At 4°C, water has minimum volume and maximum density.

Core Definitions:

• • Boyle's Law: The volume of a fixed mass of gas is inversely proportional to its pressure at a constant temperature (p ∝ 1/V).
• • Charles's Law: The volume of a fixed mass of gas is directly proportional to its absolute temperature at a constant pressure (V ∝ T).
• • Root Mean Square Speed (c_rms): The square root of the mean of the squares of the speeds of gas molecules.

Equations:

• • Ideal Gas Equation: pV = nRT
• • Kinetic Theory Equation: pV = 1/3 * Nm * c_rms²
• • Average Kinetic Energy of a molecule: E_k = 3/2 * kT
• • c_rms Formula: c_rms = √(3RT / M) = √(3p / ρ)

Key Points:

• • An ideal gas has zero intermolecular attractive forces.
• • Dalton's Law of Partial Pressures: The total pressure of a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases (p = p_A + p_B + p_C).

Core Definitions:

• • Heat Capacity (C): The quantity of heat required to raise the temperature of the object by 1 K.
• • Specific Heat Capacity (c): The quantity of heat required to raise the temperature of 1 kg of a substance by 1 K.
• • Specific Latent Heat (l): The quantity of heat required to change the state of 1 kg of a substance without any change of temperature.

Equations:

• • Heat for temperature change: Q = mcΔθ
• • Heat for phase change: Q = ml
• • Newton's Law of Cooling: dQ/dt = kA(θ - θ_R) (Rate of heat loss is proportional to temperature difference with the surroundings)

Key Points:

• • During a change of state, temperature remains constant despite heat exchange.

Core Definitions:

• • Saturated Vapour: A vapour that is in equilibrium with its liquid phase (holds maximum possible vapour).
• • Dew Point: The temperature at which the water vapour present in the air is just sufficient to saturate it.
• • Relative Humidity (RH): RH = ( mass of water vapour in a given volume / mass of water vapour required to saturate the same volume at the same temperature ) × 100%

Equations:

• • Relative Humidity (Pressure based): RH = ( partial pressure of water vapour (p) / saturated water vapour pressure (P₀) ) × 100%
• • First Law of Thermodynamics: ΔQ = ΔU + ΔW
• • Work done by system (at constant pressure): ΔW = pΔV

Key Points:

• • Saturated vapours do not obey gas laws (pV = nRT).
• • At constant temperature, saturated vapour pressure does not depend on volume.

Core Definitions:

• • Conduction: Transfer of heat through atomic/molecular collisions (requires medium).
• • Convection: Transfer of heat by actual movement of fluid particles (requires medium).
• • Radiation: Transfer of heat via electromagnetic waves (requires no medium).

Equations:

Rate of heat conduction: dQ / dt = kA(θ₁ - θ₂) / l (k: thermal conductivity, A: cross-sectional area, l: length)

Key Points:

• • In a fully lagged bar, the rate of heat flow is constant at all points along the bar.