A faulty Centigrade thermometer has its U.F.P. and L.F.P....

A faulty Centigrade thermometer has its U.F.P. and L.F.P. respectively $105^{n}$ and $-10{ }^{\circ} \mathrm{C}$, What will be its reading if it is dipped in a liquid whose actual temperature is $50^{\circ} \mathrm{C}$.

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Key Concepts

Linear Interpolation in Error Correction

When an instrument displays errors that change uniformly over its range, a linear relationship can be assumed between the actual and observed values. By using the known fixed points, one can derive a linear equation (in the form y = a + bx) which allows for the correction of the instrument’s readings at any temperature by adjusting for both offset and scale error.

Fixed Points in Instrument Calibration

Fixed points are specific, reproducible physical phenomena or temperatures that are used as benchmarks when calibrating instruments. For a Centigrade thermometer, the freezing point (typically 0°C) and the boiling point (typically 100°C) of water are common choices. These known values help in formulating a relationship between the true temperature and the instrument’s erroneous readings.

Calibration of Measuring Instruments

Calibration is the process of setting and correcting a measuring instrument by comparing it with known standard values. In the context of thermometry, standard fixed points such as the freezing and boiling points of water are used to identify and correct systematic errors, ensuring that the instrument’s readings accurately reflect the true temperature.

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