Which of the following substances (with specific heat capacity provided) would show the smallest temperature change upon gaining 200.0 J of heat?

• A. Substance C: 2.00 J/g°C
• B. Substance A: 0.50 J/g°C
• C. Substance B: 1.00 J/g°C
• D. Substance D: 0.25 J/g°C

Answer: (A)

Verified step by step guidance

1. Identify the formula for calculating temperature change when a substance gains heat: \( q = mc\Delta T \), where \( q \) is the heat energy (in joules), \( m \) is the mass (in grams), \( c \) is the specific heat capacity (in J/g°C), and \( \Delta T \) is the temperature change (in °C).
2. Rearrange the formula to solve for \( \Delta T \): \( \Delta T = \frac{q}{mc} \). This equation shows that the temperature change is inversely proportional to the specific heat capacity.
3. Recognize that for a given amount of heat energy \( q \) and mass \( m \), a substance with a higher specific heat capacity \( c \) will have a smaller temperature change \( \Delta T \).
4. Compare the specific heat capacities of the substances: Substance A: 0.50 J/g°C, Substance B: 1.00 J/g°C, Substance C: 2.00 J/g°C, Substance D: 0.25 J/g°C.
5. Determine that Substance C, with the highest specific heat capacity of 2.00 J/g°C, will exhibit the smallest temperature change upon gaining 200.0 J of heat.