Thermal energy is the internal energy stored within a system, related to the movement of its microscopic particles, such as atoms and molecules. This energy measures the total kinetic and potential energies of these particles within a substance. Temperature is a measure of the average kinetic energy, meaning higher temperatures correspond to greater thermal energy. When a temperature difference exists between two systems, thermal energy transfers from the warmer system to the cooler one. The change in thermal energy, often called heat transfer, represents the amount of energy that moves into or out of a substance.
The Formula for Thermal Energy Change
The change in thermal energy, symbolized as \(Q\), is calculated when a substance changes temperature without undergoing a phase change. This calculation uses the specific heat capacity formula, \(Q = mc\Delta T\), which links the energy transferred to the material’s physical properties. Here, \(Q\) is the quantity of heat transferred, and \(m\) is the mass of the substance being heated or cooled. The term \(c\) stands for the material’s specific heat capacity, which indicates how resistant the substance is to temperature changes. Finally, \(\Delta T\) represents the observed change in temperature of the material.
Defining the Variables and Units
To use the specific heat formula, it is necessary to understand the definitions and standard units for each variable. The mass, represented by \(m\), quantifies the amount of matter in the sample and must be expressed in kilograms (\(\text{kg}\)).
The specific heat capacity, \(c\), defines the energy required to raise the temperature of a unit mass of a substance by one degree. Water, for example, has a high specific heat capacity, requiring more energy to heat up compared to metals like iron. The standard SI unit for specific heat capacity is Joules per kilogram per Kelvin or Celsius, written as \(\text{J}/(\text{kg}\cdot\text{K})\) or \(\text{J}/(\text{kg}\cdot^\circ\text{C})\).
\(\Delta T\) represents the change in temperature, calculated by subtracting the initial temperature from the final temperature (\(T_{\text{final}} – T_{\text{initial}}\)). A positive \(\Delta T\) indicates the substance gained thermal energy, while a negative value shows it lost energy. The temperature change can be measured in either degrees Celsius (\(^\circ\text{C}\)) or Kelvin (\(\text{K}\)), as the magnitude of a one-degree change is identical in both scales.
Step-by-Step Calculation Example
Consider an example of heating \(0.5\) kilograms of water from an initial temperature of \(20^\circ\text{C}\) to a final temperature of \(80^\circ\text{C}\). The first step is to identify the known values from the problem and the established physical constants.
The mass (\(m\)) is \(0.5\text{ kg}\), the initial temperature (\(T_{\text{initial}}\)) is \(20^\circ\text{C}\), and the final temperature (\(T_{\text{final}}\)) is \(80^\circ\text{C}\). The specific heat capacity (\(c\)) of liquid water is approximately \(4184\text{ J}/(\text{kg}\cdot^\circ\text{C})\), which is a value found in standard reference tables.
The next step involves calculating the change in temperature, \(\Delta T\), by subtracting the initial from the final temperature: \(80^\circ\text{C} – 20^\circ\text{C}\), which results in a \(\Delta T\) of \(60^\circ\text{C}\). This positive value confirms that thermal energy is being absorbed by the water.
Substitute these values into the formula \(Q = mc\Delta T\). The calculation becomes \(Q = (0.5\text{ kg}) \times (4184\text{ J}/(\text{kg}\cdot^\circ\text{C})) \times (60^\circ\text{C})\). The units of kilograms and degrees Celsius cancel out, leaving the result in Joules, the standard unit for energy.
Multiplying these values yields \(Q = 125,520\text{ J}\). This means \(125,520\text{ Joules}\) of thermal energy must be transferred to the \(0.5\text{ kg}\) of water to raise its temperature by \(60^\circ\text{C}\).