Thermal Expansion-how much has the ocean expanded

[endurance12]

The ocean’s average temperature has risen by approx 0.375°C over the century. Use this value to estimate by how much the ocean water might have expanded in items of percentage increase.

This is what i started doing but I do not think this is right.
Coefficient of Cubical Thermal Expansion (Y)= change in volume (dv)/ Initial volume (v) * change in temp (dt)

Coefficient of volume expansion of water= 207*10^-6 per deg C
Linear coefficient = 1/3 cubical coefficient
=1/3*207*10^-6
= 6.9*10^-6%
But i am not getting the right answer I do not think. Can you please help me?

 

[CWatters]

Does the question ask for a percentage increase in depth (linear) or volume (cubic)?

 

[endurance12]

i believe volume

 

[haruspex]

Coefficient of volume expansion of water= 207*10^-6 per deg C
Linear coefficient = 1/3 cubical coefficient
=1/3*207*10^-6

If you think the question is asking for volumetric expansion, why divide by 3?

= 6.9*10^-6%

That's off by 3 orders of magnitude. Try the last step again.

 

[Nickie]

I would like to clarify that thermal expansion is a complex phenomenon that involves not only temperature change, but also other factors such as salinity and pressure. Therefore, it is not accurate to estimate the expansion of the ocean based on just the average temperature increase.

However, to address the question, we can use the linear coefficient of thermal expansion of water, which is approximately 2.07 x 10^-4 per degree Celsius. This means that for every 1 degree Celsius increase in temperature, water will expand by 2.07 x 10^-4 of its original volume.

Based on the given information of the ocean's average temperature increase of 0.375°C over a century, we can estimate that the ocean water may have expanded by approximately 0.00078% (0.375 x 2.07 x 10^-4) over the same time period. This is a very small percentage increase, but it can have significant impacts on sea levels and ocean currents.

It is important to note that this is just an estimate and the actual expansion of the ocean may vary depending on other factors. Further research and analysis are needed to accurately determine the expansion of the ocean due to thermal effects.