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JAMB Physics 2018 Paper

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Question : 23

Total: 87

The linear expansivity of brass is 2 x 10

^{-5}

^{-1}

. If the volume of a piece of brass is 15.00cm at 0°C, what is the volume at 100°C

16.03cm $^{3}$
15.09cm $^{3}$
16.00cm $^{3}$
15.03cm $^{3}$

Solution:

Concept:

For a solid, the volume expansivity

\gamma

is three times the linear expansivity

\alpha

:

\gamma = 3\alpha

.

Explanation:

Given

\alpha = 2 \times 10^{-5}\,\mathrm{C}^{-1}

and

V_1 = 15.00\,\mathrm{cm}^3

at

0^\circ\mathrm{C}

.

First, find

\gamma

:

\gamma = 3\alpha = 3 \times (2 \times 10^{-5}) = 6 \times 10^{-5}\,\mathrm{C}^{-1}

.

Temperature change:

\Delta\theta = 100 - 0 = 100^\circ\mathrm{C}

.

Use the volume expansion formula:

V_2 = V_1(1 + \gamma\Delta\theta)

.

Substitute values:

V_2 = 15.00\,[1 + (6 \times 10^{-5})(100)] = 15.00(1.006)

.

Therefore,

V_2 = 15.09\,\mathrm{cm}^3

.

Answer:

The volume at

100^\circ\mathrm{C}

is

15.09\,\mathrm{cm}^3

.

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