Comprehensive Guide to Thermal Energy, Heat Transfer, and Internal Energy

Types of Thermal Energy Transfer

There are three distinct types of thermal energy transfer: conduction, convection, and radiation. Thermal conduction (Wärmeleitung) occurs when materials have different levels of thermal conductivity, such as the difference between a metal spoon and a wooden spoon. In the particle model, this process is visualized as faster-moving particles colliding with their slower neighbors, causing them to move more vigorously. Gases and air are generally poor thermal conductors. The fundamental driver for this form of energy transfer is a temperature difference between two points.

Convection (Konvektion) involving flowing gases or liquids provides a mechanism where the medium itself carries the energy. This process is not possible in solids. Self-acting convection occurs when air or water is heated, perhaps by a flame, causing it to expand and rise. This creates a vacuum (Unterdruck) that draws in cooler air from the sides. Forced convection occurs through external means, such as a fan. A practical example is a candle flame, where the air to the side of the flame remains cool for a long time, while the air above the flame becomes hot even at a significant distance.

Radiation (Strahlung) allows energy to be transferred thermally without the need for matter via electromagnetic radiation. Depending on the temperature, such as the energy output of the human body, this occurs in the infrared range, which is invisible to humans. At higher temperatures, radiation may occur in the visible spectrum, such as with a glowing wire, or in the ultraviolet (UV) range. Energy loss through radiation can be minimized using material like silver or gold emergency blankets (Rettungsdecke) because they reflect the radiation.

Dynamics of Cooling and Heating Processes

During a cooling process, the temperature changes in a characteristic way. The temperature initially drops sharply and then decreases less and less as it approaches a limit value, which is the ambient or environmental temperature. Theoretically, the temperature never actually reaches this limit. In an warming process, the temperature initially rises sharply and then increases at a decreasing rate until it nears the ambient temperature. Mathematically, these processes belong to exponential relationships. For example, a recorded cooling process showed a half-life (Halbwertszeit) of $1200\,s$, which is equal to $20\,minutes$. This half-life represents the fixed interval of time in which half of the cooling or warming progress is completed.

The amount of energy transferred to the environment is directly related to the temperature difference; the larger the temperature difference, the greater the amount of energy released. This explains the curve of the resulting graphs. In the particle model, temperature is defined as a measure of the average kinetic energy of the particles in a material. Higher temperatures correspond to faster particle movement. The absolute zero point exists at $0\,K$ (Kelvin), which is equivalent to $-273.15^{\circ}C$.

Internal Energy and Aggregated States

Internal energy (Innere Energie) represents the total energy contained within a body. It consists of two components: the kinetic energy (Kinetische Energie) of the particles, which correlates with temperature, and the potential energy (Potenzielle Energie) of the particles, which arises from the interactions and bonds between them. When the temperature of a body increases, kinetic energy is being added. However, energy can also be added without a temperature increase, specifically during phase changes like melting or evaporation. In these cases, the energy is used to loosen the bonds between particles, thereby increasing the potential energy. For instance, water vapor at $100^{\circ}C$ possesses more internal energy than liquid water at $100^{\circ}C$.

During the melting process of ice, the temperature remains constant at approximately $0^{\circ}C$ until all the ice has melted. This plateau occurs because the energy supplied is being used to break the tight cohesion of the particles. It requires $334\,kJ$ of energy to melt $1\,kg$ of ice. Similarly, evaporating water requires energy, specifically $2260\,kJ$ for each $1\,kg$ of water. The specific amount of energy required depends on both the substance and its mass. Conversely, when a substance solidifies (Erstarrung) or condenses (Kondensieren), internal energy is released into the environment. This latent energy release explains why steam burns are particularly dangerous and why steam is effective for heating milk in coffee machines.

Thermodynamic Definitions and Heat

The term "heat" (Wärme) has different meanings in everyday language versus physics. In everyday use, it often describes a feeling or is used synonymously with temperature. However, in physics, heat specifically describes the energy that is transferred due to a temperature difference. Heat is therefore a process of transfer rather than a state of a body. It is physically incorrect to say "The body has a lot of heat." Instead, one should say the body has a high temperature or a high amount of internal energy.

Energy calculations can be performed using various formulas. The power $P$ of a device, measured in Watts, determines the energy flow rate as defined by $P = \frac{\Delta E}{\Delta t}$, where $\Delta E$ is the energy supplied and $\Delta t$ is the time elapsed. To calculate the minimum energy required to heat a specific mass $m$ of a substance with a specific heat capacity $c$ by a temperature difference $\Delta T$, the formula used is $\Delta E = c \times m \times \Delta T$. This is considered a minimum amount because a portion of the energy is always "lost" to the environment during the process.

Specific Heat Capacity and Mixture Calculations

Specific heat capacity (spezifische Wärmekapazität) can be determined through experiments, such as mixing substances of different temperatures. For example, if $40\,g$ of cooking oil at a room temperature of $20.4^{\circ}C$ is mixed with $60\,g$ of hot water at $82^{\circ}C$, and the resulting mixture reaches a temperature of $66^{\circ}C$, the energy lost by the water is assumed to be equal to the energy gained by the oil. By using the known specific heat capacity of water, one can calculate $\Delta E$ and then solve for the specific heat capacity of the oil. In another scenario, a glass marble weighing $6\,g$ heated to $72^{\circ}C$ was placed into $43\,g$ of water at $18.8^{\circ}C$, resulting in a final water temperature of $20^{\circ}C$. These calculations require consistent use of units and account for potential measurement inaccuracies, such as those caused by heat loss to the containers or the environment.

Experiments involving steady energy input, such as heating oil with a $100\,W$ hot plate, demonstrate the relationship between supplied energy and temperature change. For $250\,g$ of oil starting at $20^{\circ}C$, temperature data points included $34.0^{\circ}C$ at $1\,min$, $48.0^{\circ}C$ at $2\,min$, $62.5^{\circ}C$ at $3\,min$, and $76.5^{\circ}C$ at $4\,min$. Plotting these values on a coordinate system with supplied energy ($kJ$) against temperature difference ($K$) helps determine if a proportional relationship exists. A proportional relationship is indicated if the data points form a straight line passing through the origin (Ursprungsgerade). The slope of this line corresponds to specific physical properties of the substance.

Irreversible Processes and Energy Degradation

While everyday language suggests that energy is "consumed," physics dictates that energy is only converted. However, we speak of energy degradation (Energieentwertung) when energy is released into the environment in a way that it cannot be recovered. These processes are called irreversible (unumkehrbar). Real-world processes are typically irreversible. An example is a "Flummi" (super ball) that does not return to its original height after a bounce; a portion of its potential energy is converted into thermal energy through friction and impact, which is then irreversibly lost to the surroundings.

Questions and Discussion

The following tasks and questions were provided for further study and verification of understanding: What power in Watts does a device have, and how much energy in Joules is transferred per second? How many Kilojoules ($kJ$) are transferred? Given a mass of water in $kg$, the starting temperature, and the target temperature, how long would it take to heat the water using an immersion heater or a stove? Calculate the required energy amount first and then the time needed.

Additional exercises included mixed tasks from the IServ system: IServ 7 (Energy during melting), IServ 8 (Internal energy, temperature, and heat), and IServ 6 (Mixture tasks for those who finish early). Students were directed to read pages 36-39 of the textbook and complete exercise 1 on page 39. A Kahoot challenge was also provided with the Pin $05005153$.