The linear expansivity of brass is 2 x 10^{-5} ^{}{C}^{-1}. If the volume of piece of brass is 10cm³ at 0^{}C. What will be its volume at 100^{}C?

Correct Answer is : 10.06cm3³3

Correct Answer is : 10.06cm3³3

Test Index

JAMB Physics 2020 Paper

Question : 28

Total: 38

^{-5}

^{\circ}\mathrm{C}^{-1}

^{3}

^{\circ}

^{\circ}

Solution:

Concept:

For solids, the volume expansivity

\gamma

is three times the linear expansivity

\alpha

, and the new volume is given by

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

Explanation:

Find volume expansivity:

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

Initial volume:

V_1 = 10 \, \mathrm{cm}^3

0^{\circ}\mathrm{C}

Temperature change:

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

Apply the volume expansion formula:

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

V_2 = 10\bigl(1 + 6 \times 10^{-5} \times 100\bigr)

Compute:

6 \times 10^{-5} \times 100 = 6 \times 10^{-3} = 0.006

V_2 = 10(1 + 0.006) = 10 \times 1.006 = 10.06 \, \mathrm{cm}^3

Answer:

The volume at

100^{\circ}\mathrm{C}

10.06 \, \mathrm{cm}^3

Correct option: A. 10.06 cm $^3$ .

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