What is the heat capacity of a substance?

Question

BlackTom AI · Accepted Answer

Heat capacity is the amount of heat energy required to raise the temperature of a whole object or sample by 1 degree Celsius (or 1 kelvin).

1) Relevant concepts:
- Heat capacity (C) is an extensive property of an object and depends on the amount of substance present.
- Specific heat capacity (c) is the heat capacity per unit mass (an intensive property).
- Units: joules per degree Celsius (J/°C) or joules per kelvin (J/K). The relation between heat added Q, heat capacity C, and temperature change ΔT is Q = C·ΔT.

2) Step-by-step reasoning:
- Start from the defining equation: Q = C · ΔT.
- If the temperature change ΔT is 1°C, then Q = C · 1°C = C.
- Therefore C equals the heat energy required to produce a 1°C temperature rise of the entire object.

3) Intermediate steps shown:
- Given ΔT = 1°C,
- Q = C × ΔT = C × 1°C,
- So Q = C (meaning C has the same numerical value as the heat, in joules, needed for that 1°C increase).

4) Why this answer is correct:
- The definition of heat capacity is exactly the proportionality constant linking heat added to temperature change for an object. By definition, the energy required to raise the temperature by one degree equals the heat capacity itself. This is the standard textbook definition.

5) Why other possible choices would be incorrect:
- “Specific heat capacity” would be per unit mass (J/kg·°C), not the heat needed for the whole object.
- “Molar heat capacity” is per mole (J/mol·°C).
- “Heat required to change phase” or “rate of heat transfer” describe different concepts (latent heat and thermal conductivity, respectively), not heat capacity.

Conclusion: The correct interpretation is that heat capacity is the heat needed to raise the temperature of a substance (the whole object or sample) by 1°C, which matches the provided answer.

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