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JAMB Physics 2014 Paper

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Question : 41

Total: 41

A glass bottle of initial volume 2 x 104 cm3 is heated from 20oC to 50oC. If the linear expansivity of glass is 9 x 10-6K-1, the volume of the bottle at 50oC is

20016.2cm³
20005.4cm³
20008.1cm³
20013.5cm³

Solution:

Concept:

The volume expansion of the bottle depends on the volume expansivity, which is three times the linear expansivity.

Explanation:

Volume expansivity,

\gamma = 3\alpha

.

Given

\alpha = 9 \times 10^{-6} \, \mathrm{K}^{-1}

, so

\gamma = 3(9 \times 10^{-6}) = 27 \times 10^{-6} \, \mathrm{K}^{-1}

.

Temperature change,

\Delta \theta = 50 - 20 = 30 \, \mathrm{K}

.

Initial volume,

V_1 = 2 \times 10^4 \, \mathrm{cm}^3

.

Change in volume:

\Delta V = \gamma V_1 \Delta \theta

\Delta V = (27 \times 10^{-6})(2 \times 10^4)(30)

\Delta V = 16.2 \, \mathrm{cm}^3

.

Final volume,

V_2 = V_1 + \Delta V = 2 \times 10^4 + 16.2 = 20016.2 \, \mathrm{cm}^3

.

Answer:

A.

20016.2 \, \mathrm{cm}^3

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