To determine which substance is most likely to heat up the fastest, we need to consider the specific heat capacity of each substance. Specific heat capacity is a measure of how much heat energy is required to raise the temperature of a substance by one degree Celsius. Substances with lower specific heat capacities will heat up faster because they require less energy to increase their temperature.
Here are the specific heat capacities for the given substances:
- Water: [tex]\(4.19 \, \text{J/g} \cdot ^{\circ}\text{C}\)[/tex]
- Copper: [tex]\(0.39 \, \text{J/g} \cdot ^{\circ}\text{C}\)[/tex]
- Aluminum: [tex]\(0.90 \, \text{J/g} \cdot ^{\circ}\text{C}\)[/tex]
- Dry Air: [tex]\(1.01 \, \text{J/g} \cdot ^{\circ}\text{C}\)[/tex]
To identify which substance heats up the fastest, we look for the substance with the lowest specific heat capacity among these options.
Comparing the specific heat capacities:
- Water: [tex]\(4.19 \, \text{J/g} \cdot ^{\circ}\text{C}\)[/tex]
- Copper: [tex]\(0.39 \, \text{J/g} \cdot ^{\circ}\text{C}\)[/tex]
- Aluminum: [tex]\(0.90 \, \text{J/g} \cdot ^{\circ}\text{C}\)[/tex]
- Dry Air: [tex]\(1.01 \, \text{J/g} \cdot ^{\circ}\text{C}\)[/tex]
From this comparison, it is clear that copper has the lowest specific heat capacity ([tex]\(0.39 \, \text{J/g} \cdot ^{\circ}\text{C}\)[/tex]).
Therefore, since copper has the lowest specific heat capacity, it is the substance that is most likely to heat up the fastest.
