Question

Copper is used in building the integrated circuits, chips, and printed circuit boards for computers. When \(228 \mathrm{~J}\) of heat are absorbed by \(125 \mathrm{~g}\) of copper at \(22.38^{\circ} \mathrm{C}\), the temperature increases to \(27.12^{\circ} \mathrm{C}\). What is the specific heat of copper?

Short answer

Answer: The specific heat of copper is approximately \(0.384 \frac{\mathrm{J}}{\mathrm{g}\cdot^{\circ}\mathrm{C}}\).

Step-by-step solution

Identify the given values and the unknown value

In this problem, we are given the following values: - Heat absorbed \((q) = 228 \mathrm{~J}\) - Mass of copper \((m) = 125 \mathrm{~g}\) - Initial temperature \((T_i) = 22.38^{\circ} \mathrm{C}\) - Final temperature \((T_f) = 27.12^{\circ} \mathrm{C}\) The unknown value that we want to find is the specific heat of copper \((c)\).

Calculate the change in temperature

To find the change in temperature, we will subtract the initial temperature from the final temperature: \(\Delta T = T_f - T_i\). \(\Delta T = 27.12^{\circ} \mathrm{C} - 22.38^{\circ} \mathrm{C} = 4.74^{\circ} \mathrm{C}\)

Rearrange the heat capacity formula to solve for the specific heat

We will rearrange the heat capacity formula, \(q = mc\Delta T\), to solve for the specific heat \((c)\): \(c=\frac{q}{m\Delta T}\)

Plug the values into the formula and solve for the specific heat

Now we can plug in the given values and solve for the specific heat of copper: \(c=\frac{228\mathrm{~J}}{125\mathrm{~g}\times 4.74^{\circ}\mathrm{C}}\) \(c\approx 0.384 \frac{\mathrm{J}}{\mathrm{g}\cdot^{\circ}\mathrm{C}}\) The specific heat of copper is approximately \(0.384 \frac{\mathrm{J}}{\mathrm{g}\cdot^{\circ}\mathrm{C}}\).

Key concepts

Heat Transfer in Chemistry

Understanding heat transfer in chemistry is essential for predicting and controlling temperature changes during reactions or when substances absorb or release heat. Heat is a form of energy transfer between objects or systems due to a temperature difference. When a substance, such as copper, absorbs heat, the energy causes the particles within the material to move more vigorously, resulting in a rise in temperature.
The specific heat capacity, commonly referred to as specific heat, is a property that quantifies how much heat energy is required to raise the temperature of a certain mass of a substance by one degree Celsius (or one Kelvin). Mathematically, it's represented by the formula:
\[ c = \frac{q}{m\Delta T} \]
where \( c \) is the specific heat, \( q \) is the amount of heat absorbed or released, \( m \) is the mass of the substance, and \( \Delta T \) is the change in temperature. This calculation is particularly crucial in fields like materials chemistry, where understanding and optimizing heat transfer can lead to the development of better thermal management systems in electronics or more efficient energy storage solutions.

Thermodynamics in Materials

The study of thermodynamics in materials involves the principles that govern the conversion of heat energy to and from other forms of energy and how it affects matter. All materials have thermal properties that determine how they respond to changes in temperature, of which specific heat is a key factor.

For example, metals like copper have relatively lower specific heats compared to water, meaning they heat up and cool down more quickly for a given amount of heat transfer. This concept can be applied to understand the performance and safety of materials in various applications, such as the thermal management in electronic devices. An object's specific heat can be indicative of the extent to which it can buffer changes in temperature, acting as a thermal reservoir or a conductor.
In the context of designing circuits and components for electronics, materials with a balance of good electrical conductivity and appropriate thermal characteristics are selected. Copper, being a common choice, helps in dissipating heat efficiently, thereby protecting the device from overheating. Thermodynamics provides us with the framework to quantify, manipulate, and utilize these properties, making it a cornerstone of material science and engineering.

Chemical Properties of Copper

Copper is a chemical element with distinctive physical and chemical properties that make it useful in a wide array of applications, particularly in electrical wiring and electronics due to its excellent conductivity. It is a relatively soft, malleable, and ductile metal with a reddish-orange color, often used in alloy form to enhance strength without compromising conductivity.

As a metal, copper's low specific heat capacity is a relevant property, reflecting its ability to transfer heat efficiently, which is crucial in applications that involve heat dissipation. Recognized for its corrosion resistance, copper forms a characteristic green patina, known as verdigris, when exposed to the elements over time. The thermal conductivity of copper is among the highest of commercial metals, which is why, in part, it is chosen for heat exchangers, radiators, and cooling systems.
In chemistry, copper is known to have two primary oxidation states: +1 and +2. The +2 oxidation state is the more stable form and is typically encountered in most copper compounds. These compounds are usually colored and are used in a variety of chemical reactions and catalytic processes. By understanding the chemical properties of copper, scientists and engineers can harness its capabilities in numerous technological and industrial applications.