Temperature Scales and Linear Thermometry
For a property that varies linearly with temperature, equal fractions of the interval between two reproducible fixed points represent equal temperature intervals, independent of the numerical scale labels.
Why this shows up in the exam
Faulty thermometer correction · Custom temperature-scale conversion · Gas and resistance thermometer calibration
Learn the idea
A linear thermometer maps a thermometric property between two fixed calibration points. Think of every linear scale as the same temperature line with different labels: subtract the lower fixed point, divide by the interval, and then relabel the fraction on the target scale.
🧠 Memory hook: Calibrate fractions first; scale labels come last.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- (X-X_l)/(X_u-X_l) = (T-T_l)/(T_u-T_l) — linear fixed-point calibration; all four fixed-point values must belong to the stated scales
- F = (9/5)C + 32 — Celsius-to-Fahrenheit conversion for temperature readings
- Delta F = (9/5)Delta C — conversion of temperature intervals; the 32-degree offset is not used
How to approach it
- 1Write both fixed points on each scale
- 2Form the dimensionless interval fraction
- 3Convert the requested reading or interval and check the fixed points
Common slip-ups that cost marks
- •Adding 32 to a temperature difference
- •Using absolute zero as a fixed point when none is given
- •Assuming a graphical option is verified without its source figure
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A wire 1 m long and cross-sectional area 2 mm^2 extends by 1 mm under a 200 N load. Find Young modulus.
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