What is the difference between the heat capacity (C) and the specific heat (c)?

Question

BlackTom AI · Accepted Answer

To tackle this question, I will compare the meanings of heat capacity C and specific heat c, and then evaluate each statement accordingly.
Option a: 'C is the amount of heat to raise the capacity by 1°C, c is the amount of heat to raise the capacity of 1 kg of mass by 1°C.' This is a muddled description. It incorrectly talks about raising the 'capacity' by 1°C, which is not a standard way to define heat capacity. It also confuses the idea that specific heat relates to 1 kg, not the overall capacity; the phrasing makes both terms ill-defined.
Option b: 'C is the amount of heat to raise the capacity by 1°C, c is the amount of heat to raise the capacity of 1 kg of mass by 1°C.' Here, the phrase 'raise the capacity' is again problematic. Additionally, it suggests C and c are about increasing capacity, which is not how heat capacity is defined. The statement mislabels the physical quantities and their roles, leading to conceptual error.
Option c: 'C is the amount of heat to raise the temperature of 1 kg of mass by 1°C, c is the amount of heat to raise the temperature of an object by 1°C.' This is closer but still flawed. It asserts C is linked to a fixed 1 kg mass, whereas C is the total heat required to raise the temperature of the entire object, not per kilogram. It also defines c as the heat to raise the temperature of an object by 1°C, which omits the per-mass specification and can be misleading since c is specifically per unit mass.
Option d: 'C is the amount of heat to raise the temperature of an object by 1°C, c is the amount of heat to raise the temperature of 1 kg of mass by 1°C.' This aligns with standard definitions. Heat capacity C tells us how much heat is needed to raise the object's temperature by 1°C (for the whole object). Specific heat c (often symbolized as c) is the amount of heat required to raise the temperature of 1 kilogram of material by 1°C, reflecting per-mass scaling. The units and relationships match: q = C ΔT for the object, and q = m c ΔT for a mass m. 
In summary, the incorrect options misstate what ‘capacity’ and ‘specific heat’ refer to, either by misusing the term 'capacity,' misplacing per-mass qualifiers, or by perverting which quantity is tied to per-mass versus a whole object. The only option that correctly distinguishes C as the total heat for a temperature change of the object and c as the per-kilogram heat for a given temperature change is option d.

What is the difference between the heat capacity (C) and the specific heat (c)?Single choice

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