At 25.0 degree C, the radius of a solid aluminum sphere is 7.50 cm. At what temp

Question

At 25.0 degree C, the radius of a solid aluminum sphere is 7.50 cm. At what temperature will the volume of the sphere have increased by 4.00%? What is the increase in the sphere's radius if it is heated to 200 degree C? Assume alpha = 22.2 times 10^-6 K^-1 and beta = 66.6 times 10^-6 K^-1. A copper cube with density 8.96 times 10^3 kg/m^3 and mass 17.0 kg at 33.0 degree C is heated to 180 degree C. What is the density of the copper cube at this new temperature? (Give your answer to at least three significant figures.) What is the mass of the copper cube at this new temperature?

Explanation / Answer

1)
a)
from the given data

V' = V + V*beta*(T2 - T1)

V + 4.00% V = V + V*beta*(T2 - T1)

0.04*V = V*66.6*10^-6*(T2 - 25)

0.04 = 66.6*10^-6*(T - 25)

T2 = 626 degrees celsius <<<<<<<<<----------------Answer

b)
V' = V + V*beta*(T2 - T1)

(4/3)*pi*R'^3 = (4/3)*pi*R^3 + (4/3)*pi*R^3*beta*(T2-T1)

R'^3 = 7.5^3 + 7.5^3*66.6*10^-6*(200 - 25)

R' = 7.53 cm <<<<<<<<<----------------Answer

2)
a) for copper, beta = 49.9*10^-6 K^-1

V' = V*(1 + beta*(T2-T1))

V'/m = (V/m)*(1 + beta*(T2-T1))

1/d' = 1/(8.96*10^3)*(1 + 49.9*10^-6*(180-33))

d' = 8.89*10^3 kg/m^3 <<<<<<<<<----------------Answer

b) same. i.e 17.0 kg <<<<<<<<<----------------Answer

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