Thermal Energy, Heat, and Work

Understanding temperature, heat transfer, and the laws of thermodynamics

Introduction to Thermal Physics

Thermal physics is the study of heat, temperature, and energy transfer. It explains how thermal energy moves between systems and how it affects the properties of matter. Thermodynamics, a branch of thermal physics, provides the fundamental laws that govern these processes and help us understand everything from engines to refrigerators.

Temperature and Thermal Energy

Temperature is a measure of the average kinetic energy of particles in a substance. Thermal energy, also called internal energy, is the total energy of all the particles in a system. These concepts are fundamental to understanding how thermal systems behave.

Temperature Scales

Several temperature scales are used in science:

  • Celsius (°C): Water freezes at 0°C and boils at 100°C at standard pressure
  • Fahrenheit (°F): Water freezes at 32°F and boils at 212°F at standard pressure
  • Kelvin (K): The SI unit of temperature; 0 K is absolute zero (the theoretical temperature at which particles have zero kinetic energy)
Temperature Conversion
\[K = °C + 273.15\] \[°F = \frac{9}{5}°C + 32\] \[°C = \frac{5}{9}(°F - 32)\]
Example 1: Temperature Conversion

Convert 25°C to Kelvin and Fahrenheit.

\[K = 25°C + 273.15 = 298.15 \text{ K}\]

\[°F = \frac{9}{5}(25°C) + 32 = 45 + 32 = 77°F\]

Heat Transfer

Heat is the transfer of thermal energy from a warmer object to a cooler one. It is not a substance but a process. Heat flows spontaneously from higher temperature to lower temperature until thermal equilibrium is reached.

Methods of Heat Transfer

  1. Conduction: Transfer of heat through direct contact between particles
  2. Convection: Transfer of heat by the movement of fluids (liquids or gases)
  3. Radiation: Transfer of heat through electromagnetic waves
Heat Transfer by Conduction
\[H = \frac{kA(T_2 - T_1)t}{L}\]
Where:
  • \(H\) = heat transferred (in joules, J)
  • \(k\) = thermal conductivity of the material (W/(m⋅K))
  • \(A\) = cross-sectional area (in m²)
  • \(T_2 - T_1\) = temperature difference (in K or °C)
  • \(t\) = time (in s)
  • \(L\) = thickness of the material (in m)
Example 2: Heat Conduction

A glass window pane has an area of 2 m² and a thickness of 0.5 cm. If the inside temperature is 20°C and the outside temperature is 5°C, how much heat is lost through the window in 1 hour? (Thermal conductivity of glass = 0.8 W/(m⋅K))

\[H = \frac{kA(T_2 - T_1)t}{L}\]

\[H = \frac{0.8 \times 2 \times (20 - 5) \times 3600}{0.005} = \frac{0.8 \times 2 \times 15 \times 3600}{0.005}\]

\[H = 1.728 \times 10^7 \text{ J} = 17.28 \text{ MJ}\]

Specific Heat and Phase Changes

Specific heat capacity is the amount of heat required to raise the temperature of 1 kg of a substance by 1°C or 1 K. Different materials have different specific heat capacities, which explains why some materials heat up faster than others.

Heat and Temperature Change
\[Q = mc\Delta T\]
Where:
  • \(Q\) = heat energy transferred (in joules, J)
  • \(m\) = mass (in kg)
  • \(c\) = specific heat capacity (J/(kg⋅K) or J/(kg⋅°C))
  • \(\Delta T\) = change in temperature (in K or °C)
Example 3: Heating Water

How much heat is needed to raise the temperature of 2 kg of water from 20°C to 80°C? (Specific heat capacity of water = 4,186 J/(kg⋅°C))

\[Q = mc\Delta T = 2 \times 4,186 \times (80 - 20)\]

\[Q = 2 \times 4,186 \times 60 = 502,320 \text{ J} = 502.32 \text{ kJ}\]

Phase Changes

When a substance changes phase (e.g., from solid to liquid or liquid to gas), heat is transferred without a change in temperature. This heat is called latent heat.

Heat for Phase Change
\[Q = mL\]
Where:
  • \(Q\) = heat energy transferred (in joules, J)
  • \(m\) = mass (in kg)
  • \(L\) = latent heat (J/kg)
Common latent heats for water:
  • Latent heat of fusion (melting/freezing): 334,000 J/kg
  • Latent heat of vaporization (boiling/condensing): 2,260,000 J/kg
Example 4: Melting Ice

How much heat is required to convert 0.5 kg of ice at 0°C to water at 0°C?

\[Q = mL = 0.5 \text{ kg} \times 334,000 \text{ J/kg} = 167,000 \text{ J} = 167 \text{ kJ}\]

Laws of Thermodynamics

The laws of thermodynamics are fundamental principles governing energy transfer and transformation in thermal 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 the concept of temperature as a fundamental property.

First Law of Thermodynamics

Energy cannot be created or destroyed, only transferred or converted from one form to another. This is the principle of conservation of energy applied to thermodynamic systems.

First Law Equation
\[\Delta U = Q - W\]
Where:
  • \(\Delta U\) = change in internal energy (in J)
  • \(Q\) = heat added to the system (in J)
  • \(W\) = work done by the system (in J)
Example 5: First Law Application

A gas in a cylinder absorbs 800 J of heat and expands, doing 500 J of work. What is the change in internal energy of the gas?

\[\Delta U = Q - W = 800 \text{ J} - 500 \text{ J} = 300 \text{ J}\]

Second Law of Thermodynamics

In any closed system, entropy (a measure of disorder) tends to increase over time. Heat naturally flows from hot to cold, not vice versa. This law explains why some processes are irreversible and sets limits on the efficiency of heat engines.

Third Law of Thermodynamics

As the temperature approaches absolute zero, the entropy of a pure crystalline substance approaches zero. This law establishes a reference point for entropy and explains why absolute zero is theoretically unattainable.

Heat Engines and Efficiency

A heat engine is a device that converts thermal energy to mechanical work by exploiting temperature differences. Understanding heat engine efficiency is crucial for power generation and energy conservation.

Thermal Efficiency
\[\eta = \frac{W}{Q_h} = 1 - \frac{Q_c}{Q_h}\] \[\text{For a Carnot engine: } \eta_{Carnot} = 1 - \frac{T_c}{T_h}\]
Where:
  • \(\eta\) = efficiency (dimensionless, often expressed as percentage)
  • \(W\) = work output (in J)
  • \(Q_h\) = heat input from the hot reservoir (in J)
  • \(Q_c\) = heat rejected to the cold reservoir (in J)
  • \(T_h\) = absolute temperature of the hot reservoir (in K)
  • \(T_c\) = absolute temperature of the cold reservoir (in K)
Example 6: Heat Engine Efficiency

A heat engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. What is the maximum possible efficiency?

\[\eta_{max} = 1 - \frac{T_c}{T_h} = 1 - \frac{300 \text{ K}}{500 \text{ K}} = 1 - 0.6 = 0.4 \text{ or } 40\%\]

Applications of Thermal Physics

Understanding thermal physics is essential for many technological applications and daily life:

Power Generation
  • Steam engines and turbines
  • Nuclear reactor cooling systems
  • Solar thermal power plants
HVAC Systems
  • Heating system design
  • Air conditioning efficiency
  • Building insulation optimization
Refrigeration
  • Refrigerators and freezers
  • Heat pump technology
  • Cryogenic applications
Materials Science
  • Thermal expansion studies
  • Insulation material development
  • Heat treatment of metals
Environmental Science
  • Weather forecasting models
  • Climate change research
  • Atmospheric energy balance
Electronics
  • Cooling system design
  • Thermal management in computers
  • Electronic component reliability

Key Concepts Summary

  • Temperature: Measure of average kinetic energy of particles
  • Heat transfer: Conduction, convection, and radiation
  • Specific heat: \(Q = mc\Delta T\) - energy needed to change temperature
  • Phase changes: \(Q = mL\) - energy for state transitions
  • First Law: \(\Delta U = Q - W\) - conservation of energy
  • Heat engine efficiency: \(\eta = 1 - \frac{T_c}{T_h}\) - maximum theoretical efficiency