Percentage Uncertainty in Temperature Difference

Steps:

• Temperature rise ΔT = 100°C - 40°C = 60°C.
• Absolute uncertainty in ΔT = uncertainty in initial + uncertainty in final = 0.5°C + 0.5°C = 1°C (error propagation for subtraction).
• Percentage uncertainty = (1°C / 60°C) × 100% ≈ 1.7%.

Why D is correct:

• Error propagation for temperature difference adds absolute uncertainties, doubling the single-reading error to 1°C, yielding 1.7% for the 60°C rise per standard uncertainty rules.

Why the others are wrong:

• A: Ignores propagation; treats 0.5°C uncertainty on full 100°C scale.
• B: Uses single 0.5°C uncertainty on 60°C rise (0.5/60 × 100% ≈ 0.8%).
• C: Applies 0.5°C uncertainty to initial 40°C reading (0.5/40 × 100% = 1.25% ≈ 1.3%).

Final answer: D