Rise in sea level due to increased temp. on earth

In summary: I think I have finally got it now! I will definitely keep your advice in mind for future problems. Thank you again for your help and for explaining it in a secondary-school way. It really helped me grasp the concept better. In summary, the problem asks for an equation for sea level rise using the expansion coefficient and the change in temperature. The key is to use algebra and postpone plugging in data until the last step. By considering the fact that surface area is constant and using the equation V=h•A, we can find the expression for dV/dT and solve for h, which represents the increase in depth due to sea level rise.
  • #1
Donna14
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Homework Statement



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The Attempt at a Solution



I'm really struggling to understand how to solve this problem.
I guess I need to know the volume and surface of the sea on earth?
But I'm honesty a bit lost as we don't have a textbook etc.
 

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  • #2
No, you don't need the volume or surface area to solve the problem. All you need is the depth. Solve the problem symbolically - that is using algebra. Do not plug in any data until you reach the very last step of your solution (This is very important piece of advice. You should always, ALWAYS, postpone plugging in any data as much as possible for any problem not just that problem. In fact I tell my students to sit on their calculators until they are done solving problems. Often times it is not needed at all). You will see that any reference to the volume or surface area of the ocean cancels out of your equations.
 
  • #3
Thank you for your good advice. I'll will keep that it mond whiles making the exercises.
But I'm still totale lost on how to derive an equation with the geven information... Sorry I'm new to this, but really willing to understand.
 
  • #4
Write down the expression for the volume in terms of surface area and average depth. Find the expression for dV/dT. Divide one by the other (that's when the area cancels out), and set it equal to the expansion coefficient. solve the equation (isolate the sea level rise). plug in the data now and calculate the sea level rise. It is really a fairly simple exercise.

In fact, you should've posted that in the introductory physics homework forum. This is the advanced physics homework forum intended for advanced physics homework questions...
 
  • #5
Im feeling so dumb...
Volume is surface area sea x average depth isn't it?
Im just not getting how to find de expression for dV/dT
Where to incorporate the T.

Wished I would have you as a teacher for a bit here!

Im really sorry I have to ask so much...
 
  • #6
Donna14 said:
Im feeling so dumb...
Volume is surface area sea x average depth isn't it?
Im just not getting how to find de expression for dV/dT
Where to incorporate the T.

Wished I would have you as a teacher for a bit here!

Im really sorry I have to ask so much...

Yes that's right. V=A*h where A is the surface area and h is the average depth. Now replace V with (A*h) in dV/dT and consider the fact that the area A is constant. what do you get for dV/dT?
 
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  • #7
V=h•A
dV=A

(1/h•A)•(A/dT)=expansion coëfficiënt
A/(h•A•dT)=E.c.
h•A•dT=A/E.c.
h=A/(E.c.•dT•A)
h=1/(E.c.•dT)

Does this look like something?

And represents this h now the increase and not the total depth?
 
  • #8
Donna14 said:
V=h•A
dV=A

(1/h•A)•(A/dT)=expansion coëfficiënt
A/(h•A•dT)=E.c.
h•A•dT=A/E.c.
h=A/(E.c.•dT•A)
h=1/(E.c.•dT)

Does this look like something?

And represents this h now the increase and not the total depth?

dV = A is incorrect. It doesn't even have the correct units. dV is a volume. A is an area. Try again. If the surface area doesn't change but the depth has a variation dh what happens to the depth?
 
  • #9
I'm going to look at the problem in a secondary-school way (which is what it deserves!)
Say you have a single column exactly 1 square meter in area.
The area will not change, because other water columns are immediately next to it.
The 0.00015 per degree C is then just a fractional increase in the depth (per degree C).

The interesting part is part (c), why the actual rise was much less than the expected rise. Some possibilities are (i) the spill-out effect, the lateral area of the ocean increases slightly when sea level rises, (ii) the time scale of deep ocean circulation, which is many hundreds of years, (iii) non-linearities in the seawater equation of state: perhaps the expansion coefficient is smaller where the pressure is great, or where the temperature is low to begin with, (iv) maybe a warmer atmosphere kept more of Earth's water in a vapor state. I leave it to you to evaluate these by doing some reading.
 
  • #10
V=h•A
dV=dh•A

(1/h•A)•(A•dh/dT)=expansion coëfficiënt
(dh/h)•(1/dT)=E.c.
dh=E.c•dT•h

I think I have got the correct answer now...
 
  • #11
Donna14 said:
V=h•A
dV=dh•A

(1/h•A)•(A•dh/dT)=expansion coëfficiënt
(dh/h)•(1/dT)=E.c.
dh=E.c•dT•h

I think I have got the correct answer now...

That's it. Easy, wasn't it?
 
Last edited:
  • #12
Thank you so much for your patience!
 

What is causing the rise in sea level?

The rise in sea level is primarily caused by global warming and the resulting increase in temperature on Earth. This is due to the greenhouse effect, where certain gases in the atmosphere trap heat and cause the Earth's surface temperature to rise.

How much has sea level risen in recent years?

According to the National Oceanic and Atmospheric Administration, sea level has risen by an average of 3.2 millimeters per year since 1993. This may not seem like much, but it adds up over time and can have significant impacts on coastal areas.

What are the effects of rising sea level?

Rising sea level can have a variety of effects, including coastal flooding, erosion, and saltwater intrusion into freshwater sources. It can also harm marine life and impact the livelihoods of people living in coastal areas.

Can we stop or reverse the rise in sea level?

While we cannot completely stop or reverse the rise in sea level, we can take steps to mitigate its effects. This includes reducing our carbon emissions and implementing sustainable practices to slow down global warming.

What can be done to adapt to rising sea level?

To adapt to rising sea level, coastal communities can implement measures such as building sea walls and levees, elevating buildings, and creating natural barriers like wetlands. However, these measures may not be feasible or effective in the long term, so addressing the root cause of rising sea level is crucial.

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