A mercury barometer is calibrated at

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

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

, when it reads exactly

76.0\,\text{cm}

. The barometer is later used in a laboratory whose temperature is

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

. The coefficient of volume expansion of mercury is

\beta_{\text{Hg}} = 1.8\times10^{-4}\,^{\circ}\text{C}^{-1}

and the linear coefficient of expansion of the glass tube is

\alpha_{\text{glass}} = 9.0\times10^{-6}\,^{\circ}\text{C}^{-1}

. (i) Derive an expression for the corrected barometric height

h_{\text{true}}

in terms of the observed height

h_{\text{obs}}

, the temperature change

\Delta T

\beta_{\text{Hg}}

and

\alpha_{\text{glass}}

. (ii) Using the derived expression, calculate the true atmospheric pressure corresponding to the observed height

h_{\text{obs}} = 75.0\,\text{cm}

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

. (iii) Evaluate the percentage error that would occur if the thermal expansion of mercury and glass were ignored.