Derive an expression for the length of the mercury column in a liquid-in-glass…

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

Problem

Derive an expression for the length

l_\theta

of the mercury column in a liquid-in-glass thermometer at temperature

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

in terms of the initial bulb volume

V_0

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

, the uniform capillary cross-sectional area

A

, the real volume expansion coefficient of mercury

\gamma_m

and the cubical expansion coefficient of glass

\gamma_g

. (Assume the length of the column at

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

is negligible compared with

l_\theta