Question

The ice and steam points on a thermometer correspond to X and 50mm respectively. A temperature of 60degree celcius corresponds to 52mm on the thermometer. Calculate the value of X

Answer 1

Let:

$$\begin{array}{l} T(60) = 60{}^{\circ} \mathrm{C} \\ T(100) = 100{}^{\circ} \mathrm{C} \\ T(x) = 0{}^{\circ} \mathrm{C} \\ L(100) = 50 \mathrm{~mm} \\ L(60) = 52 \mathrm{~mm} \\ L(x) = ? \\ \end{array}$$

Find how many mm on $1{}^{\circ}\mathrm{C}$

$$\begin{array}{l} L(1{}^{\circ} \mathrm{C}) = \frac{L(100) - L(60)}{T(100) - T(60)} = \frac{50 - 52}{100 - 60} = -\frac{2}{40} = -0.05 \mathrm{~mm} \\ L(x) = L(100) - L(1{}^{\circ} \mathrm{C}) * (T(100) - T(x)) = 50 - (-0.05 * 100) = 55 \mathrm{~mm} \\ \end{array}$$

Answer: the value of X is: 55 mm