Specific heat at constant pressure (Cp): Choose the correct SI unit for Cp used in thermodynamics and heat transfer.

Introduction / Context:
The unit of specific heat capacity at constant pressure (Cp) is fundamental to energy balances, heat exchanger design, and process simulations. Correct unit usage ensures consistent calculations of enthalpy changes and sensible heat loads.

Given Data / Assumptions:

• Sought: SI unit for Cp.
• Cp relates heat input to temperature change per unit mass at constant pressure.

Concept / Approach:
By definition, Cp = (heat added at constant P) / (mass * temperature rise). In SI, heat is measured in joules (J), mass in kilograms (kg), and temperature in kelvin (K). Therefore, Cp units are J/(kg·K).

Step-by-Step Solution:

Verification / Alternative check:
Enthalpy change for sensible heating: Δh = ∫ Cp dT, which has units J/kg—consistent only if Cp is J/kg·K integrated over K.

Why Other Options Are Wrong:

• W/m^2·°C and W/m·K: These are heat flux or thermal conductivity units, not specific heat.
• J/m^3·K: This is volumetric heat capacity, not specific heat per unit mass.

Common Pitfalls:
Mixing mass-based Cp with molar heat capacity (J/mol·K). Always confirm whether a property is mass-based or molar-based.

Final Answer:
J/kg·K