Question

Estimate the fractional change in the volume of Earth ,ocean due to an average temperature change of 1°C. Use the fact that average depth of ocean is 4m to estimate change of depth?β=2.07x10^-4,°C

Answer 1

Probably there is an easier way...

Explanation:

I may be wrong but I think this is a thermal expansion problem...
The change in volume `DeltaV` should be equal to the original volume `V_0` times the expansion coefficient `beta` times the change in temperature `DeltaT`:
`DeltaV=V_0*beta*DeltaT`
So:
`V-V_0=V_0*beta*DeltaT`
`(V-V_0)/V_0=beta*DeltaT`
`V/V_0-1=beta*DeltaT`
`V/V_0=beta*DeltaT+1=2.07×10^-4×1+1=1.000207`
I suppose a positive change in temperature...
So the new volume should be `1.000207` times the initial...or a `0.01%` change in volume.

For the change in depth:
I would try to find the initial volume of water `V_0` using the radius of Earth (from the literature).

Then I would use this `V_0` to find the new volume `V` and so the new radius `h` and from there `h-r` as the new depth...