A special thermometer is to be calibrated using a quartz bulb instead of ordinary glass

PHYSICS · Subjective · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A special thermometer is to be calibrated using a quartz bulb instead of ordinary glass. The quartz has a coefficient of linear expansion

0.4\times10^{-6}\,\text{K}^{-1}

. The thermometric liquid is mercury with real volumetric expansion coefficient

1.82\times10^{-4}\,\text{K}^{-1}

. The internal radius of the uniform capillary is

0.20\,\text{mm}

and the bulb volume at

0\,^{\circ}\text{C}

0.60\,\text{cm}^3

. (a) Derive an expression for the length

L

of the mercury column at a temperature

T\,^{\circ}\text{C}

measured from the ice point. (b) Using your expression, find the length at the steam point (

100\,^{\circ}\text{C}

) if the column length at the ice point is

1.5\,\text{cm}

. (c) If a linear scale is still engraved on the stem between

0\,^{\circ}\text{C}

and

100\,^{\circ}\text{C}

, determine the error (in degrees Celsius) in the reading at

100\,^{\circ}\text{C}

introduced by neglecting the expansion of quartz.