Convert Any Linear Temperature Scale with One Ratio
Every linear temperature scale is fixed by two reference points, the ice point and the steam point, so converting between two scales only needs the position of a reading between those two points. Celsius, Fahrenheit and any invented scale in an exam question follow the same rule.
Temperature Scales and Conversions is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
One ratio converts every linear scale
For two linear scales X and Y with lower and upper fixed points, (X - LFPx) / (UFPx - LFPx) = (Y - LFPy) / (UFPy - LFPy). If thermometer X has its ice point at 15 and steam point at 75, and thermometer Y has 20 and 100, the fundamental intervals are 60 and 80 divisions, so one division of X equals 4/3 divisions of Y once the zero offsets are removed.
Write the ratio first and substitute afterwards; guessing a factor and an offset separately is how sign errors creep in.
Celsius and Fahrenheit
A graph of Celsius against Fahrenheit is therefore a straight line with slope 5/9 that meets the Fahrenheit axis at 32 (where C = 0) and passes through the point (212 F, 100 C).
When a question shows several candidate curves, discard any that are curved, have a negative slope, or miss the 32 F / 0 C and 212 F / 100 C anchor points.
Kelvin, Celsius and Fahrenheit differences
Convert to kelvin (T = C + 273) before using any gas law, efficiency or radiation formula, but you may use Celsius directly for differences, as in calorimetry.
OlympIQ exam lens
- ✓Any linear scale is fixed by its ice point and steam point; compare the reading's position between them on both scales
- ✓Subtract the lower fixed point first, then scale by the ratio of fundamental intervals, then add the other scale's lower fixed point
- ✓F = (9/5)C + 32; Celsius and Fahrenheit readings coincide at -40
- ✓Use kelvin in gas laws, efficiency and radiation formulas; Celsius differences equal kelvin differences
Do not convert by multiplying the reading by the ratio of interval sizes alone. A scale whose ice point is not zero (such as 15 or 39) needs its offset removed first, so subtract the lower fixed point, scale by the ratio of fundamental intervals, and only then add the other scale's lower fixed point.
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