Question

You hold a gram of copper in one hand and a gram of aluminum in the other. Each metal was originally at \(0{ }^{\circ} \mathrm{C}\). (Both metals are in the shape of a little ball that fits into your hand.) If energy is transferred to both at the same rate, which will warm to your body temperature first? Explain your answer.

Short answer

Copper will warm to body temperature first.

Step-by-step solution

Understanding the Problem

You have one gram each of copper and aluminum, both initially at 0°C. Energy is added to both at the same rate, and we need to find out which metal will reach body temperature (approximately 37°C) first.

Identifying Key Concepts

To determine how fast each metal warms up, we need to consider the specific heat capacity of each metal. The specific heat capacity is the amount of heat required to raise the temperature of one gram of a substance by 1°C.

Comparing Specific Heat Capacities

The specific heat capacity of copper is approximately 0.385 J/g°C, while for aluminum it is approximately 0.897 J/g°C. This means aluminum requires more energy than copper to increase its temperature by the same amount.

Applying the Concept

Since energy is added at the same rate to both metals, copper, having a lower specific heat capacity, will require less energy to reach body temperature compared to aluminum. Thus, copper will warm up faster.

Conclusion

Copper, with a lower specific heat capacity, will reach the body temperature of 37°C before aluminum, given the same rate of energy transfer to both metals.

Key concepts

Thermal Properties of Metals

When it comes to understanding how metals respond to heat, their thermal properties are key. Metals like copper and aluminum have different thermal conductivities and specific heat capacities. The specific heat capacity is crucial here because it tells us how much energy (in joules) is needed to increase the temperature of a given mass of a substance by 1°C.
For metals, this is an indicator of their ability to store heat. Copper has a specific heat capacity of about 0.385 J/g°C, meaning it does not need a lot of energy to get warm. Aluminum, on the other hand, has a higher specific heat capacity of 0.897 J/g°C, implying it requires more energy to rise in temperature.
These properties help explain why different metals feel hotter or cooler to the touch even if they are at the same temperature—copper heats up and cools down faster than aluminum because it can quickly take in or release heat energy.

Energy Transfer

Energy transfer is a fundamental concept in physics involving the movement of energy from one place or object to another. In the context of this problem, we are adding energy to both metals at the same rate. But what exactly does that mean?
When energy is transferred to a substance, it raises the temperature of that substance. The rate of energy transfer is crucial because it affects how quickly a substance reaches a new temperature state. Here, we have two metals absorbing energy at equal rates, which allows us to focus entirely on their specific heat capacities to determine which one heats up faster.

• Since copper's specific heat capacity is lower, it takes fewer joules to increase its temperature by each degree Celsius compared to aluminum.
• Therefore, given the same rate of energy input, copper reaches the given higher temperature more rapidly.

This concept of energy transfer not only applies to metals but is a universal principle affecting all matter.

Comparative Heating

Comparative heating is the process of analyzing how different substances respond to the same heat conditions. In this exercise, it involves examining how copper and aluminum, two common metals, react to being heated at the same rate.
The core of the comparison lies in their specific heat capacities, which dictate how quickly or slowly each metal can warm up. With both metals starting at 0°C and being subject to the same energy input, copper, with its lower specific heat capacity, increases in temperature faster.

• This efficient heating is why copper is often preferred in applications requiring quick thermal responses, such as in cooking and electrical wiring.
• Conversely, aluminum, with its ability to absorb more heat without rapidly changing temperature, is valuable in situations where controlled heating is beneficial.

Understanding comparative heating helps in selecting the right material for specific tasks, demonstrating the importance of specific heat capacity in practical applications.