Which of the following substances is most likely to heat up the fastest when the same amount of heat is applied to each?

• A. Copper (c = 0.385 J/g·K)
• B. Aluminum (c = 0.897 J/g·K)
• C. Ethanol (c = 2.44 J/g·K)
• D. Water (c = 4.18 J/g·K)

Answer: (A)

Verified step by step guidance

1. Understand that the rate at which a substance heats up when the same amount of heat is applied depends on its specific heat capacity, denoted as \(c\). The specific heat capacity is the amount of heat required to raise the temperature of 1 gram of a substance by 1 Kelvin (or 1 degree Celsius).
2. Recall the formula relating heat added (\(q\)), mass (\(m\)), specific heat capacity (\(c\)), and temperature change (\(\Delta T\)): \[q = m \times c \times \Delta T\]
3. Since the problem states the same amount of heat (\(q\)) is applied to each substance and assuming equal masses, rearrange the formula to solve for temperature change: \[\Delta T = \frac{q}{m \times c}\]
4. Notice that \(\Delta T\) is inversely proportional to the specific heat capacity \(c\). This means the substance with the smallest specific heat capacity will experience the largest temperature change (heat up the fastest) for the same amount of heat applied.
5. Compare the given specific heat capacities: Copper (0.385 J/g·K), Aluminum (0.897 J/g·K), Ethanol (2.44 J/g·K), and Water (4.18 J/g·K). Identify the substance with the lowest \(c\) value, which will heat up the fastest.