Heat Capacity vs. Water Equivalent — Are Their Numerical Values the Same? Judge the statement: “The numerical value of the thermal capacity (heat capacity) of a body and its water equivalent are the same.”

Introduction / Context:
Heat capacity (thermal capacity) and water equivalent are related but distinct concepts used in calorimetry. Confusing them leads to unit mistakes and wrong interpretations of experimental results.

Given Data / Assumptions:

• Heat capacity C_body = m_body * c_body with units J/K.
• Specific heat of water c_water ≈ 4186 J/(kg·K) in SI.
• Water equivalent W_eq is defined as mass of water that has the same heat capacity as the body.

Concept / Approach:
By definition, W_eq (kg) satisfies C_body = W_eq * c_water, so W_eq = C_body / c_water. Therefore, numerical equality holds only in unit systems where c_water is numerically 1 (e.g., 1 cal/(g·K) in CGS-calorie units). In SI, c_water ≠ 1, so the numerical values differ unless coincidentally scaled.

Step-by-Step Solution:
Write C_body = m_body * c_body.Set C_body = W_eq * c_water ⇒ W_eq = C_body / c_water.Since c_water ≈ 4186 in SI, W_eq and C_body cannot have the same numerical value in SI units.

Verification / Alternative check:
Example: if C_body = 2093 J/K, then W_eq = 2093/4186 ≈ 0.5 kg of water. The numbers (2093 vs. 0.5) are not equal, proving the general statement false in SI.

Why Other Options Are Wrong:
Agreeing would only be valid in a special unit system (calorie-gram) and is not generally true; the question asks for general correctness.

Common Pitfalls:
Dropping units and comparing “numbers” alone; mixing unit systems; assuming c_water = 1 in SI.

Final Answer:
Disagree