Rise in sea level due to increased temp. on earth

[Donna14]

Homework Statement

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Homework Equations

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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.

 

[dauto]

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.

 

[Donna14]

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.

 

[dauto]

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...

 

[Donna14]

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...

 

[dauto]

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?

 

[Donna14]

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?

 

[dauto]

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?

 

[az_lender]

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.

 

[Donna14]

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...

 

[dauto]

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?

 

[Donna14]

Thank you so much for your patience!