Identify the incorrect temperature conversion relation:\nChoose the option that is wrong (others are correct reformulations).

Introduction / Context:
Accurate temperature conversions are essential across thermodynamics, heat transfer, and instrumentation. Rømer, Rankine, Celsius, Fahrenheit, and Kelvin scales often appear in legacy data or vendor specifications; choosing the correct formula avoids significant calculation errors.

Given Data / Assumptions:

• Kelvin–Celsius: K = °C + 273.15 (≈ 273 for quick estimates).
• Rankine–Fahrenheit: °R = °F + 459.67.
• Linear scale relations: °F = (9/5)°C + 32 and °C = (5/9)(°F − 32).
• Temperature differences: ΔK = Δ°C = (9/5)Δ°F.

Concept / Approach:
Check each formula against the standard relations. Remember that offsets differ between pairs: Rankine and Fahrenheit share degree size but different zero; Kelvin and Celsius share offset at zero. Differences (not absolute values) convert without offsets, but magnitudes scale by 9/5 between °F and °C/K.

Step-by-Step Evaluation:

Verification / Alternative check:
Test with °C = 0: (d) gives °F = 1.8 × 17.778 ≈ 32, as expected. For (a), if °F = 0, formula would give °R = 273, but the actual Rankine at 0 °F is 459.67 °R.

Why Other Options Are Wrong or Right:

• (a) Wrong due to incorrect zero offset.
• (b)–(d) are correct relations for differences or equivalent algebraic forms.

Common Pitfalls:
Confusing absolute temperatures with temperature differences; mixing the Kelvin and Rankine offsets; rounding offsets too aggressively.

Final Answer:
°R = °F + 273