Which of the following units is the S.I. unit of heat capacity?

Analyze the question: We need the S.I. unit of heat capacity (not specific heat capacity, which is a common trap).

Concept:

• Heat capacity (C) is the quantity of heat needed to raise the temperature of a whole body by 1 K.
• Formula: C = Q / Δθ
• Specific heat capacity (c) is heat per unit mass per unit temperature change: c = Q / (mΔθ)

Solution:

• Q is measured in joules (J)
• Δθ is measured in kelvin (K)

So the unit of heat capacity is:

C = Q / Δθ = J / K = J K⁻¹

Checking the options:

• A. J kg⁻¹ is the unit of specific latent heat, not heat capacity.
• B. J kg⁻¹ K⁻¹ is the unit of specific heat capacity.
• C. J K⁻¹ is the unit of heat capacity. ✔
• D. J g⁻¹ K⁻¹ is also a specific heat capacity unit, and it is not S.I. because grams are not the S.I. mass unit.

Tip: Look for the word "specific". If it is there, the unit includes "per kg" (kg⁻¹). If it is not, as with plain heat capacity, there is no mass in the unit. So:

• Heat capacity → J K⁻¹
• Specific heat capacity → J kg⁻¹ K⁻¹
• Specific latent heat → J kg⁻¹