A piece of copper alloy with a mass of 85.0 g is heated from \(30.0^{\circ} \mathrm{C}\) to \(45.0^{\circ} \mathrm{C}\) . During this process, it absorbs 523 \(\mathrm{J}\) of energy as heat. a. What is the specific heat of this copper alloy? b. How much energy will the same sample lose if it is cooled to \(25^{\circ} \mathrm{C} ?\)

Thermodynamics is a vital aspect of our daily lives and it dictates how energy is transformed and transferred between objects and systems. In essence, thermodynamics is the study of the relationships between heat, work, temperature, and energy. When considering the heating of any substance, such as a copper alloy in the exercise, understanding the laws of thermodynamics helps in predicting how the substance will behave with energy input.

For the copper alloy, as its temperature rises upon heating, we observe one of the fundamental concepts of thermodynamics—energy transfer. Energy, in the form of heat, is transferred to the copper, causing the molecules to move more briskly and thus increasing its temperature. The specific heat capacity, which is a measure of how much energy is needed to raise the temperature of a unit mass by one degree, is intrinsic to the material, making it a key thermodynamic property for calculations.

Energy transfer is pivotal when discussing changes in temperature. It is this transfer of energy that causes objects to heat up or cool down. To calculate the energy transfer, we harness the concept of specific heat, denoted by the symbol 'c'. The specific heat capacity can be understood as a substance's thermal inertia - a measure of how much the temperature of the object resists change when it absorbs or loses heat.

The exercise demonstrates energy transfer where 523 J of energy is absorbed by the copper alloy. Using the specific heat calculation formula, we can quantify this transfer. In everyday situations, the objects around us are continuously exchanging heat with their environments, following the second law of thermodynamics, which in simple terms states that heat flows from warmer to cooler objects until thermal equilibrium is achieved. Understanding energy transfer and specific heat is not just crucial in solving textbook problems but also in real-world applications - from designing thermal systems to cooking a meal.

Temperature change is a direct indication of energy exchange in a system. In our exercise, the copper alloy's temperature change signifies that it has either absorbed or lost heat. The temperature change ($\mathrm{\Delta T}$) in the specific heat equation is what determines the amount of heat transferred, together with the mass and specific heat capacity of the substance.

Understanding temperature change is crucial not just in thermodynamics but also in everyday life. Weather patterns, cooking food, and even the operation of refrigerators are all governed by the principles of temperature change. In the context of the exercise, calculating the temperature drop when the copper alloy is cooled from