Answer:
Change in volume / volume = 3 K change in temperature
K = 24E-6 / deg C coefficient of linear expansion
R = 4.1 cm
dR / R = 24E-6 * 120 dec C = 2.88E-3
V = 4/3 pi R^3
dV = 4 pi R^2 dR
dV / V = 3 dR / R = 2.88E-3 * 3 = 8.6E-3 = .86%
The percentage change in volume of the aluminum sphere at the given cubic expansivity is 0.9%.
The percentage change in the volume of the aluminum sphere is determined by applying cubic expansivity formula of the aluminum.
V₁ = ⁴/₃πr³
where;
V₁ = ⁴/₃π(0.041)³
V₁ = 2.887 x 10⁻⁴ m³
[tex]\beta = \frac{\Delta V}{V_1 \Delta T}[/tex]
where;
[tex]\Delta V = \beta V_1 \Delta T\\\\\Delta V = (75 \times 10^{-6} )(2.887 \times 10^{-4})(150 - 30)\\\\\Delta V = 2.6 \times 10^{-6} \ m^3[/tex]
[tex]\% (V)= \frac{\Delta V}{V_1} \times 100\%\\\\\% (V)= \frac{2.6 \times 10^{-6}}{2.887 \times 10^{-4}} \times 100\%\\\\\% (V)= 0.9 \ \%[/tex]
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