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 rises 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

Write down the given values.

We have the following values: Heat absorbed: \(q = 228 J\) Mass of copper: \(m = 125 g\) Initial temperature: \(T_1 = 22.38^{\circ}C\) Final temperature: \(T_2 = 27.12^{\circ}C\)

Calculate the change in temperature.

To calculate the change in temperature, we subtract the initial temperature from the final temperature: \(\Delta T = T_2 - T_1\). \(\Delta T = 27.12^{\circ} C - 22.38^{\circ} C = 4.74^{\circ} C\)

Use the heat transfer formula to find the specific heat of copper.

The formula for heat transfer is \(q = mc\Delta T\), and we want to find the specific heat of copper (\(c\)). To solve for \(c\), we can rearrange the formula: \(c = \frac{q}{m\Delta T}\) Now, plug in the values we found in steps 1 and 2: \(c = \frac{228 \mathrm{J}}{125 \mathrm{g} \cdot 4.74^{\circ} \mathrm{C}} \approx 0.384 \frac{\mathrm{J}}{\mathrm{g} \cdot ^{\circ}\mathrm{C}}\)

Report the specific heat of copper.

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

Key concepts

Heat Transfer

Heat transfer is a fundamental concept in physics, dealing with the movement of thermal energy from one body or substance to another. This process can take place through various means such as conduction, convection, and radiation. In the context of the specific heat of copper, we're looking at conduction, which is the transfer of heat through a material.

Each material has a property known as 'specific heat capacity', which is a measure of how much heat energy is required to raise the temperature of a given mass of the substance by one degree Celsius. The exercise involving copper demonstrates this concept by showing that a certain amount of heat (228 J) changes the temperature of a specific mass of copper (125 g), allowing us to calculate its specific heat capacity. Understanding heat transfer is essential for solving such problems, and it also has larger implications in areas such as thermal management in electronic devices and energy efficiency in buildings.

Thermodynamics

At the heart of the study of heat transfer is thermodynamics, the branch of physics that deals with the relationship between heat and other forms of energy. Within thermodynamics, temperature change as a response to energy exchange is a key idea. In our exercise involving copper, the specific heat represents the energy required to change the temperature of one gram by one degree Celsius.

Thermodynamics tells us that this energy change is not lost but transferred, making it a central theme in energy conservation and efficiency. By calculating the specific heat of copper, we apply the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system on its surroundings. In the context of our exercise, the work done is negligible, so we essentially measure the heat added to the copper as it heats up from 22.38°C to 27.12°C.

Physical Properties of Metals

Metals have distinctive physical properties such as high electrical conductivity, malleability, ductility, and thermal conductivity. One of the significant thermal properties is the specific heat capacity, which varies from metal to metal. Copper, a highly conductive and commonly used metal in electronics, has a specific heat capacity that is relatively low compared to other substances. This means it requires less energy to increase its temperature.

The specific heat of copper is an intrinsic property reflecting how it will behave under thermal energy exchange. This characteristic is crucial for industrial applications, where control over temperature changes is essential. In electronics, for example, the ability of copper to dissipate heat efficiently is vital to prevent overheating of components, which is why it is widely used in heat sinks and cooling systems. The low specific heat capacity of copper combined with its excellent conductivity is instrumental in its selection for such applications.