Determine the specific heat of a material if a 35 g sample of the material absorbs 48 \(\mathrm{J}\) as it is heated from 298 \(\mathrm{K}\) to 313 \(\mathrm{K}\) .

Thermochemistry is a branch of chemistry that deals with the relationship between chemical reactions and changes in temperature. It's pivotal in understanding how energy in the form of heat is absorbed or released during chemical processes. For instance, when a material is heated, the energy absorbed by the material is a key thermochemical consideration. To quantify this, scientists use the concept of specific heat capacity, which is a measure of how much energy a substance can absorb as its temperature changes. Understanding thermochemistry is crucial for predicting the energy exchange in reactions and can be applied in various practical situations such as in material science and engineering.

In the given textbook exercise, specific heat calculation involves the principles of thermochemistry, where we examine the heat absorbed by a sample material and its subsequent temperature change.

When a subject, such as a sample of material, absorbs energy, its internal energy increases. Energy absorption often leads to an increase in temperature or a phase change. The extent to which a substance can absorb energy without changing phase is characterized by its heat capacity. In the context of the exercise provided, the 35g sample absorbs 48 Joules of energy, causing an increase in temperature. This energy absorption, which is crucial in calculating specific heat, does not imply a chemical reaction but rather a physical process where kinetic energy of particles increases.

An intuitive way to think about energy absorption is to consider how a sponge soaks up water. Similarly, the material soaks up heat, and by measuring this absorption, we can determine a material's specific heat capacity. This concept lays the foundation for many applications, including material design, where materials with specific thermal properties are required.

Heat capacity refers to the amount of heat energy required to raise the temperature of a substance by one degree. It is an extensive property, meaning it depends on the amount of substance present. In order to compare different substances, scientists use specific heat capacity, which is the heat required to raise the temperature of 1 gram of a substance by one degree Celsius (or one Kelvin). Specific heat capacity is thus a vital concept in thermochemistry as it describes how a material behaves when it interacts with heat.

Through the solution of our exercise, the specific heat is calculated, which is a practical expression of heat capacity for a given sample. The lower the specific heat, the less energy is needed to raise the temperature of the material, making it a good conductor of heat, while a high specific heat indicates that the material is an effective insulator.

Temperature change is a consequence of energy exchange as a form of heat. It signifies the difference in thermal energy before and after an event, such as heating or cooling. In the exercise, the sample's temperature increases from 298K to 313K, showing a temperature change of 15K. This change is a direct reflection of the heat energy absorbed by the sample and is essential in calculating the specific heat.

A deeper understanding of temperature change can help in everyday applications ranging from cooking to industrial processing. For example, chefs need to understand the specific heat of various foods to cook them properly, while engineers need to know the temperature changes materials can withstand. The concept helps in designing processes and equipment that manage temperature effectively for desired outcomes.