A \(2.50-g\) piece of wood is burned in a calorimeter that contains \(0.200 \mathrm{~kg}\) of water. The burning causes the water temperature to increase from \(22.1^{\circ} \mathrm{C}\) to \(28.7^{\circ} \mathrm{C}\). How much heat energy is released in joules? What is the energy content of the wood in joules per gram of wood?

Calorimetry is a technique used to measure the amount of heat transferred to or from an object during a chemical or physical process. This process is often performed using a device known as a calorimeter, which insulates a reaction to prevent heat loss or gain from the surroundings. In the context of the given exercise, the piece of wood is burned within a calorimeter containing water.

As the wood burns, it releases energy in the form of heat, which is absorbed by the water. By measuring the temperature increase of the water, we can determine the heat energy released by the combustion of the wood. The principle that governs this is the conservation of energy, which states that energy cannot be created or destroyed, only transferred. Therefore, the heat lost by the wood is equal to the heat gained by the water, enabling us to calculate the energy content of the wood.

Specific heat capacity, often symbolized as 'c', is a property that defines how much heat energy is needed to raise the temperature of one gram of a substance by one degree Celsius (or one Kelvin). Water, for instance, has a specific heat capacity of about 4.18 Joules per gram per degree Celsius (\(4.18 \frac{J}{g \times ^\text{o}C}\)), meaning it takes 4.18 J to raise the temperature of 1 gram of water by 1°C.

In our exercise, the specific heat capacity of water is essential for calculating the total heat energy absorbed because it dictates how much the water temperature will rise for a given amount of heat energy.

Temperature change, denoted as ΔT, is a vital parameter in calorimetry. It represents the difference between the final and initial temperatures of a system. The equation ΔT = T2 - T1 allows us to calculate this change, where T1 is the initial temperature and T2 the final temperature.

In the exercise, we observed a temperature shift in the water from 22.1°C to 28.7°C, resulting in a ΔT of 6.6°C. This temperature jump is directly related to the amount of heat added to the water; thus, understanding temperature change is integral to calculating the heat energy exchanged in a system.

Energy content of materials refers to the amount of energy stored within a substance, and can be calculated in terms of energy per unit of mass, such as Joules per gram (J/g). Materials with high energy content can release significant amounts of energy when they undergo chemical reactions, such as combustion.

In our problem, we calculate the energy content of wood by burning it and measuring the heat released. The energy content is determined by dividing the total heat energy (measured in Joules) by the mass of the wood burned (measured in grams), giving us an energy density in J/g. This measure is crucial for understanding not just the energy potential of fuels such as wood, but also for comparing the energy density of different materials.