Answer to Question #172721 in Physics for Korede

Question

A thermometer which was not accurately calibrated, indicated 0.5% at the lower fixed point and 106 at the upper fixed point. what is the time temperature when the thermometer registers 63.4c

Answer 1

The thermometer had 0.5°C at 0°C real temperature and 106°C at real 100°C. So, we can plot a graph assuming linear dependency, but it is better to find a function that connects the wrong values with real ones. Assume wrong values are along y-axis and correct are along x-axis. First, find the equation:

$$\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1},\\\space\\ \frac{y-0.5}{106-0.5}=\frac{x-0}{100-0},\\\space\\ x=\frac{100}{105.5}(y-0.5).$$

So, 63.4°C at the wrong scale (y) correspond to correct value (x) of

$$x=\frac{100}{105.5}(63.4-0.5)=59.6°\text{C}.$$