A thermometer with an arbitrary scale has the ice point at – 20° and the steam point at 180°. When the thermometer reads 5°, a centigrade thermometer will read

Engineering

Physics

Thermal Expansion

Question

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Relation between measurement of different scales

$\frac{x - L_{1}}{U_{1} - L_{1}} = \frac{y - L_{2}}{U_{2} - L_{2}}$

x and y are measurement in two scales
L₁, L₂ is ice point measurement, U₁, U₂ is steam point measurement in two scales
Applying in the given case

$\frac{5 - (- 20)}{200} = \frac{y - 0}{100}$

⟹ y = 12.5°C.