A glass bottle of internal volume at is completely filled with water at the same…

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

Problem

A glass bottle of internal volume

500\;\text{cm}^3

20\,^{\circ}\!\text{C}

is completely filled with water at the same temperature and then tightly sealed. The bottle and its contents are slowly cooled to

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

. Data: • Coefficient of volumetric expansion of glass,

\gamma_{\text{glass}} = 9\times10^{-6}\,\text{K}^{-1}

• For water above

4\,^{\circ}\!\text{C}

\gamma_{\text{water}} = 3.7\times10^{-4}\,\text{K}^{-1}

• Between

4\,^{\circ}\!\text{C}

and

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

, water expands further by

0.0002

of its volume at

4\,^{\circ}\!\text{C}

(due to its anomalous behaviour). (a) Calculate the decrease in volume of the glass bottle when the temperature falls from

20\,^{\circ}\!\text{C}

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

. (b) Calculate the net increase in volume of the water during the same temperature drop, taking the anomalous expansion into account. (c) Determine, with numerical justification, whether the bottle is likely to crack. State the reason for your conclusion. (d) Repeat part (b) assuming water behaved like an ordinary liquid with the same

\gamma_{\text{water}}

down to

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

(i.e., neglect the anomalous extra

0.0002

term). Comment briefly on the difference in outcome.

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