Question

An aluminium can of cylindrical shape contains 500 cm3 of water. The area of the inner cross section of the can is 125 cm2. All measurements refer to 10°C.
Find the rise in the water level if the temperature increases to 80°C. The coefficient of linear expansion of aluminium is 23 × 10–6 °C–1 and the average coefficient of the volume expansion of water is 3.2 × 10–4 °C–1.

Answer 1

The rise in the water level if the temperature increases to 80°C is 0.089 cm

Explanation:

Given:

The volume of water in the aluminium can be used,$V_0$ = 500 $cm^3$

Inner cross-sectional area of the can, A = 125 $cm^3$

expansion of water  Coefficient of volume, $\gamma = 3.2 \times 10^{-4}$ °$C^{-1}$

Coefficient of linear aluminium expansion$\alpha{AL}= 23 \times 10^{-6}$ °$C^{-1}$

Solution:

∆θ be the temperature change, then final volume of water

V due to expansion

${\mathrm{V}=\mathrm{V}_{0}(1+\gamma \Delta \theta)}$

${=500\left[1+3.2 \times 10^{-4} \times(80-10)\right]}$

${=500\left[1+3.2 \times 10^{-4} \times 70\right]}$

${=511.2 \mathrm{cm} 3}$

The aluminium vessel extends in its length

So, base expansion area may be neglected

Increase of water volume = 11.2 $cm^3$

volume of cylinder =11.2$cm^3$

∴ Increase in water height

=11.2125= 0.0896

= 0.089 cm

Answer 2

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0.089 will be the answer

hope it help