Near room temperature, the specific heat capacity of benzene is \(1.05 \mathrm{~J} \cdot\left({ }^{\circ} \mathrm{C}\right)^{-1} \mathrm{~g}^{-1}\). Calculate the heat nceded to raise the temperature of \(50.0 \mathrm{~g}\) of benzene from \(25.3^{\circ} \mathrm{C}\) to \(37.2^{\circ} \mathrm{C}\). (b) A \(1.0-\mathrm{kg}\) block of aluminum is supplied with \(490 \mathrm{~kJ}\) of heat. What is the temperature change of the aluminum? The specific heat capacity of aluminum is \(0.90 \mathrm{~J} \cdot\left({ }^{\circ} \mathrm{C}\right)^{-1} \cdot \mathrm{g}^{-1}\).

Calorimetry is a branch of thermodynamics dedicated to the measurement of the amount of heat energy transferred between objects, which is vital in understanding the conservation of energy principle. It involves the use of a calorimeter, an instrument that insulates a system to accurately measure the heat transfer during chemical reactions or physical changes.

For instance, when calculating the heat needed to raise the temperature of benzene in the exercise, calorimetry principles guide us to apply the specific heat capacity along with the mass and temperature change to find the correct amount of energy. This practice is intrinsic to calorimetry, enabling us to quantify the energy changes without loss or gain from the surroundings.

Students should ensure to consider whether the process is isolated from the environment to prevent external factors from influencing the outcome of the calorimetric calculations. Accurate determination hinges on the exactness of the involved measurements and the quality of the calorimeter used.

In thermodynamics, energy transfer is primarily concerned with how thermal energy moves from one body to another and what it does when it gets there. It's a core concept that illustrates how energy in the form of heat can lead to a change in temperature, phase, or even perform work on another system.

Thermal energy transfer can occur via three primary modes: conduction, convection, and radiation. Within the realm of calorimetry and exercises similar to our textbook problem, we focus on the conduction part — the direct transfer of energy through matter. This transfer is mathematically represented by the equation \(Q = m \times c \times \triangle T\), tying together mass, specific heat capacity, and temperature change.

Understanding this fundamental relationship helps students to predict the outcome of heating or cooling a substance. For instance, when supplying heat to the aluminum block in our exercise, knowing the specific heat capacity allows us to determine how much the temperature will change as a result of the energy transfer.

The process of calculating temperature change is fundamental in both theoretical and practical applications of thermodynamics. When a substance absorbs or loses heat, its temperature changes, a concept illustrated in our exercise with benzene and aluminum.

The temperature change \(\Delta T\) can be found using the relation \(\Delta T = T_{final} - T_{initial}\). In the context of the exercise, we use the formula \(Q = m \times c \times \Delta T\) to find the heat energy involved in changing the temperature of a given mass of a substance with known specific heat capacity. For solid and liquid materials like benzene or aluminum, this is often straightforward if we assume no phase change occurs.

Importantly, students should note that specific heat capacity is a property that varies with temperature but can be treated as constant over small temperature ranges, like in our exercise. Remembering to convert energy units when needed and matching them with the mass unit will ensure accurate calculations. The clarity in these step-by-step processes fosters a deeper comprehension of energy dynamics in diverse thermal systems.