Heat lost equals mass times specific heat times temperature change

Steps:

• Use heat transfer formula: thermal energy lost Q = m × c × ΔT, where c is specific heat capacity of iron.
• Temperature drops from θ1 to θ2, so ΔT = θ1 - θ2 (positive for loss).
• Mass m and c of iron are given; no phase change occurs.
• Compute Q directly with these values.

Why A is correct:

• Matches definition of heat lost: Q = m c (θ1 - θ2), from calorimetry law where heat change is proportional to mass, specific heat, and temperature difference.

Why the others are wrong:

• B: Uses (θ2 - θ1), yielding negative value, but heat loss is positive.
• C: Heat capacity of piece is m c, so m × (m c) = m² c (θ1 - θ2), incorrectly multiplies mass twice.
• D: Combines errors of B and C, with wrong sign and extra mass factor.

Final answer: A