Problem — Calibration curve

Problem

A temperature probe returns an output voltage that is linear in $T$. Two points are measured: $(0\ ^\circ\text{C},\ 10\ \text{mV})$ and $(50\ ^\circ\text{C},\ 110\ \text{mV})$. Find the calibration law $V(T)$ and use it to work out the temperature corresponding to a reading of $74\ \text{mV}$.

Solution

Slope (gradient) from the two points: $m = \frac{110 - 10}{50 - 0} = \frac{100}{50} = 2\ \frac{\text{mV}}{^\circ\text{C}}$

Intercept: for $T = 0$ we read $V = 10\ \text{mV}$, so $q = 10\ \text{mV}$.

Calibration law. $V(T) = 10 + 2\,T \quad [\text{mV}]$

Inversion to work out $T$ from a voltage reading: $T = \frac{V - 10}{2} = \frac{74 - 10}{2} = \frac{64}{2} = 32\ ^\circ\text{C}$

$\ev{V(T) = 10 + 2T\ \text{(mV)}\ ;\qquad T = 32\ ^\circ\text{C}}$

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Topics: Experimental method Skills: Reading graphs · Linearising data