By what quantity must the heat capacity of an object be divided to obtain the specific heat of that material?

Question

BlackTom AI · Accepted Answer

Question restatement: By what quantity must the heat capacity of an object be divided to obtain the specific heat of that material?

Option 1: its mass
Why this could be tempting: Specific heat is defined as the amount of heat required to raise the temperature of a unit mass, so dividing by mass seems to align with the idea of per- mass quantities.
Why it is correct: The standard definition of specific heat capacity (c) is q = m c ΔT, where q is heat, m is mass, and ΔT is change in temperature. Rearranging gives c = q/(m ΔT). Therefore, to obtain the specific heat from the heat capacity (the total heat capacity, which is the amount of heat needed to raise the temperature of the entire object by 1 degree), you divide by mass. This is the formal and widely accepted relationship in thermodynamics.

Option 2: its volume
Why this is incorrect: Volume is not part of the definition of specific heat. Two objects with the same volume but different masses can have different specific heats, and volume does not normalize heat per a quantity that characterizes the amount of material in a body.
Potential misconception addressed: Specific heat is an intensive property tied to the amount of substance, not simply the space it occupies.

Option 3: its temperature
Why this is incorrect: Temperature is the result of heat transfer, not the quantity by which heat capacity is scaled. Dividing by temperature would mix units improperly and does not reflect how much heat is needed per unit mass per degree of temperature change.

Option 4: its energy
Why this is incorrect: Heat capacity is defined in terms of energy required to raise the temperature of the object. The specific heat involves normalizing that energy by the amount of material (mass) and the temperature change. Dividing by the total energy would not yield a meaningful per-mass measure and would confound the relationship between heat, mass, and temperature change.

Summary: Among the given choices, dividing the total heat capacity by the mass correctly yields the specific heat capacity per unit mass, consistent with the fundamental equation q = m c ΔT.

By what quantity must the heat capacity of an object be divided to obtain the specific heat of that material?单项选择题

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