A glass vessel of initial volume at is completely filled with two immiscible liquids and

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

Problem

A glass vessel of initial volume

V

0\,^{\circ}\mathrm C

is completely filled with two immiscible liquids

A

and

B

, each occupying half the volume. The real coefficients of cubical expansion of the liquids are

\gamma_{rA}

and

\gamma_{rB}

respectively, while that of glass is

\gamma_{g}

. The temperature of the system is then raised uniformly by

\Delta T

. (a) Derive an expression for the volume of liquid that overflows, in terms of

V

\gamma_{rA}

\gamma_{rB}

\gamma_{g}

and

\Delta T

. (b) Using your result, calculate the overflow volume when

V = 1.0\,\mathrm L

\gamma_{rA} = 7.0\times10^{-4}\,\mathrm{K^{-1}}

\gamma_{rB} = 4.0\times10^{-4}\,\mathrm{K^{-1}}

\gamma_{g} = 2.7\times10^{-5}\,\mathrm{K^{-1}}

and

\Delta T = 30\,^{\circ}\mathrm C