the volume of an iron sphere is 3.00cm cubed after being heated from 20.0c to 600.0 c what was the initial volume of the iron sphere at 20.0c

Answer: 1cm3

Explanation:

V1 = ?

V2 = 3cm3

T1 = 20°C = 20 + 273 = 293K

T2 = 600°C = 600 + 273 = 873K

V1 / T1 = V2 / T2

V1 / 293 = 3 / 873

V1 = 293 x (3 / 873)

V1 = 1 cm3

V = 2.94cm³

The initial volume at 20°C is 2.94cm³

Explanation:

As the temperature of the iron sphere increases the volume of the sphere also increase.

Using the equation for volumetric expansion:

∆V = VαΔT

where;

V is the initial volume

α is the volumetric expansion coefficient

∆V is the change in Volume

∆T is the change in temperature

After Expansion the final volume can be written as:

Vf = V + ∆V

Vf = V + VαΔT

Vf = V (1 + αΔT)

making V the subject of formula;

V = Vf / (1+αΔT) ... 1

Given:

Vf = 3.00cm³

ΔT = 600-20 = 580

And from the test book.

α = 35.5 * 10⁻⁶K⁻¹

Substituting the values into eqn 1

V = 3.00 / (1+580 * 35.5*10^-6)

V = 3.00 / (1+0.021) = 3.00/1.021

V = 2.94cm³

The initial volume at 20°C is 2.94cm³