Thermodynamics

Thermodynamics is the branch of physics that deals with heat, temperature, and their relation to energy, work, radiation, and properties of matter. It describes how thermal energy is converted to and from other forms of energy and how it affects matter.

The study of thermodynamics emerged in the 19th century from efforts to increase the efficiency of early steam engines. Today, it has broad applications in science and engineering, from understanding climate change to designing efficient engines and refrigeration systems.

Temperature is a measure of the average kinetic energy of the particles in a substance. It determines the direction of heat flow between objects in thermal contact.

Common temperature scales include:

• Celsius (°C): Water freezes at 0°C and boils at 100°C at standard pressure
• Kelvin (K): The SI unit of temperature. 0 K is absolute zero, the theoretical temperature at which molecular motion stops. K = °C + 273.15
• Fahrenheit (°F): Water freezes at 32°F and boils at 212°F at standard pressure

Heat is the transfer of thermal energy between objects due to a temperature difference. Heat always flows from higher temperature to lower temperature unless work is done to reverse this flow.

The SI unit of heat is the joule (J), though the calorie (cal) is also commonly used (1 cal = 4.184 J).

Specific Heat Capacity is the amount of heat required to raise the temperature of 1 kg of a substance by 1 K (or 1°C). It is denoted by c and measured in J/(kg·K).

The heat Q required to change the temperature of a mass m by ΔT is:

Q = mcΔT

Different materials have different specific heat capacities. For example:

• Water: 4,186 J/(kg·K)
• Aluminum: 900 J/(kg·K)
• Iron: 450 J/(kg·K)

Latent Heat is the heat required to change the phase of a substance without changing its temperature. There are two types:

• Latent Heat of Fusion: Heat required to convert a solid to a liquid (or vice versa)
• Latent Heat of Vaporization: Heat required to convert a liquid to a gas (or vice versa)

The heat Q required for a phase change of mass m is:

Q = mL

Where L is the specific latent heat of the substance for that phase change.

Thermal Expansion is the tendency of matter to change its dimensions in response to a change in temperature. Most materials expand when heated and contract when cooled.

For linear expansion:

ΔL = αL₀ΔT

Where ΔL is the change in length, L₀ is the initial length, ΔT is the temperature change, and α is the coefficient of linear expansion.

The laws of thermodynamics describe the fundamental physical quantities (temperature, energy, and entropy) that characterize thermodynamic systems.

Zeroth Law of Thermodynamics: If two systems are each in thermal equilibrium with a third system, they are in thermal equilibrium with each other.

This law establishes temperature as a fundamental and measurable property.

First Law of Thermodynamics: Energy can neither be created nor destroyed, only converted from one form to another. For a thermodynamic system:

ΔU = Q - W

Where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.

Second Law of Thermodynamics: The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

This law explains why heat flows from hot to cold objects and why perfect heat engines are impossible.

Third Law of Thermodynamics: As the temperature of a system approaches absolute zero, the entropy of the system approaches a minimum value.

This law implies that it is impossible to reach absolute zero in a finite number of steps.

Heat can be transferred between objects or systems through three main mechanisms:

Conduction is the transfer of heat through direct contact between particles of matter, without bulk motion of the matter.

The rate of heat transfer by conduction is given by:

P = kA(T₂ - T₁)/d

Where P is the power (heat transfer rate), k is the thermal conductivity, A is the cross-sectional area, (T₂ - T₁) is the temperature difference, and d is the thickness of the material.

Convection is the transfer of heat by the bulk movement of molecules within fluids (liquids or gases).

The rate of heat transfer by convection is approximately:

P = hA(T₂ - T₁)

Where h is the convective heat transfer coefficient.

Radiation is the transfer of heat through electromagnetic waves, requiring no medium.

The power radiated by a body is given by the Stefan-Boltzmann law:

P = εσAT⁴

Where ε is the emissivity, σ is the Stefan-Boltzmann constant, A is the surface area, and T is the absolute temperature.

A thermodynamic process is the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. Common processes include:

Isothermal Process: Temperature remains constant (T = constant)

For an ideal gas: PV = constant (Boyle's Law)

Adiabatic Process: No heat is transferred between the system and its surroundings (Q = 0)

For an ideal gas: PV^γ = constant, where γ is the ratio of specific heats

Isobaric Process: Pressure remains constant (P = constant)

For an ideal gas: V/T = constant (Charles's Law)

Isochoric Process: Volume remains constant (V = constant)

For an ideal gas: P/T = constant (Gay-Lussac's Law)

Cyclic Process: The system returns to its initial state after a series of processes

Heat engines and refrigerators operate in cycles.