Answer to Question #172721 in Physics for Korede

Question #172721

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


1
Expert's answer
2021-03-18T16:52:40-0400

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:


yy1y2y1=xx1x2x1, y0.51060.5=x01000, x=100105.5(y0.5).\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=100105.5(63.40.5)=59.6°C.x=\frac{100}{105.5}(63.4-0.5)=59.6°\text{C}.



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