Specific heat capacity units (SI): Identify the correct SI unit for Cp, the specific heat capacity at constant pressure.

Introduction / Context:
Specific heat capacity at constant pressure, Cp, quantifies the energy required to raise the temperature of a unit mass of a substance by one kelvin at constant pressure. Correct units matter in energy balances, heat-exchanger design, and transient heating calculations across process engineering.

Given Data / Assumptions:

• Cp refers to a per-mass property (specific), not per-mole or per-volume.
• SI coherent units: energy in joules (J), temperature in kelvin (K), mass in kilograms (kg).

Concept / Approach:
By definition, Cp = (∂h/∂T)_p with h in J/kg (specific enthalpy) and T in K. Therefore, the unit becomes (J/kg)/K = J/kg·K. Distinguish this from thermal conductivity and heat flux units, which also include W and length dimensions but represent different physical properties.

Step-by-Step Solution:

Verification / Alternative check:
In molar form, Cp,m would be J/(mol·K) or kJ/(kmol·K). The presence of “per mass” vs “per mole” distinguishes specific vs molar heat capacity.

Why Other Options Are Wrong:

• W/m^2·K and W/m·K: these are heat transfer coefficient and thermal conductivity units, not heat capacity.
• J/m^3·K: a volumetric heat capacity, not specific (per mass) Cp.
• kJ/kmol·K: a molar heat capacity unit, not specific mass-based Cp.

Common Pitfalls:
Confusing Cp with k (thermal conductivity) or h (heat transfer coefficient); using molar units when data or balances are on a mass basis.

Final Answer:
J/kg·K