Question

Soon after Earth was formed, heat released by the decay of radioactive elements raised the average internal temperature from 300 to 3000 K, at about which value it remains today. Assuming an average coefficient of volume expansion of 3.2 × 10–5 K–1, by how much has the radius of Earth increased since the planet was formed?

Answer 1

Answer:

97.03%

Explanation:

The equation for volumetric expansion due to thermal expansion is as follows

V/Vo=(1+γΔT)

V=final volume

Vo=initial volume

γ=coefficient of volume expansion=3.2 × 10–5 K–1

ΔT=

temperature difference

assuming that the earth is a sphere the volume is given by

V=(4/3)pi R^3

if we find the relationship between the initial and final volume we have the following

$\frac{V}{Vo} =\frac{ \frac{4}{3} \pi r^{3} }{ \frac{4}{3} \pi ro^{3}}=\frac{r^{3} }{ro^{3}}$

taking into account the previous equation

r/ro=(1+γΔT)^(1/3)

r/r0=(1-3.2x10-5(3000-300))^(1/3)=

r/ro=0.9703=97.03%