Question

A 4.00-m-long cylinder of solid aluminum has a radius of 2.00 cm.

1)

If the cylinder is initially at a temperature of 4.00∘∘C, how much will the length change when the temperature rises to 30.0°C?

2)Due to the temperature increase, by how much (in %) would the density of the aluminum cylinder decrease?

3)By what percentage does the volume of the cylinder increase?

Answer 1

We have:

Length of the cylinder, L = 4 m = 400 cm

Radius of the cylinder, R = 2 cm

Change in temperature, ΔT = 30^oC - 4^oC = 26^oC

Linear expansion coefficient of aluminium, α = 24 x 10^-6 /^oC

Volume expansion coefficient of aluminium, γ = 3α = 72 x 10^-6 /^oC

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PART A:

Change in length of the cylinder (ΔL) is given by:

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PART B:

Initial volume of the cylinder is given by:

Final volume is given by:

Therefore, Percentage change in density is given by:

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PART C:

Percentage change in volume is given by:

>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

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