Definition check (cp): “The amount of heat required to raise the temperature of unit mass of a gas by 1 degree at constant pressure is called the specific heat at constant pressure.” Is this definition correct?

Introduction / Context:
Specific heats quantify how much heat is needed to change a substance’s temperature under specified constraints. For gases, two common constraints are constant volume (cv) and constant pressure (cp). Correctly recognizing these definitions is fundamental for applying the first law and for analyzing common processes like heating in ducts or cylinders.

Given Data / Assumptions:

• Unit mass basis (per kilogram).
• Temperature change of 1 degree (Kelvin or Celsius increment), with constant pressure maintained.
• No phase change during the temperature rise.

Concept / Approach:
By definition, cp is the heat added per unit mass per degree of temperature increase when pressure is held constant. For ideal gases, cp is related to cv and the specific gas constant R by cp − cv = R, but the definition itself does not require ideal behavior; real gases also have a cp defined at a given state and pressure path, though its value may vary with T and p.

Step-by-Step Solution:

Verification / Alternative check:
In a constant-pressure calorimeter, the measured heat divided by mass and temperature rise gives cp directly, confirming the operational meaning of the definition.

Why Other Options Are Wrong:

• False: Contradicts standard thermodynamic terminology.
• Only true for ideal gases / only true at 0°C: cp exists more generally; while its value varies, the definition remains valid.

Common Pitfalls:
Confusing cp with cv; forgetting that cp can depend on temperature and pressure for real gases.

Final Answer:
True