Physics Help Forum Sunlight Radiation on lake of ice (how long time take ice to melt) Exam soon Help!:)

 Mar 27th 2018, 03:36 AM #1 Junior Member   Join Date: Mar 2018 Posts: 1 Sunlight Radiation on lake of ice (how long time take ice to melt) Exam soon Help!:) Hi Everyone, I am new here and I hope I can get help here. Sunlight with intensity (600 w/m^2) Occurs an ice-covered lake. 70 % of the intensity absorbed of ice, which is 1.4 cm thick. How long time take to melt the ice? I know those formulas (not including in questions): P = I 4 (pi) r^2. for ice melt: dQ/dt = d/dt (m x Lf) = d/dt [ (p=density) x V x lf) (Lf = 334 KJ/kg) Thank you very much for helping me as soon as possible.
 Mar 27th 2018, 06:09 AM #2 Senior Member   Join Date: Apr 2017 Posts: 392 formulas , formulas .... no wonder you've got nowhere we are told 70% of the 600w is absorbed by the ice ...so that means every square meter absorbs 420 W ... that's 420J /sec The ice is 1.4 cm thick , so find out the mass in 1 sq meter (about 14 kg) then find how many joules it takes to melt this mass of ice .... and divide by 420 to get the number of seconds .
Mar 28th 2018, 04:02 AM   #3
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The approach Oz suggested is absolutely fine. Just some extra comments on the formulas:

 Originally Posted by Adeeb I know those formulas (not including in questions): P = I 4 (pi) r^2.
This is the equation to get the irradiance (per unit area), P, at a certain distance, r, away from a point source with a total irradiance, I. That equation isn't going to be helpful here because you don't have a point source of radiation in your problem; you're already given the irradiance per unit area.

Note that $\displaystyle 4 \pi r^2$ is the surface area of a sphere.

 for ice melt: dQ/dt = d/dt (m x Lf) = d/dt [ (p=density) x V x lf) (Lf = 334 KJ/kg)
This is an equation that's calculating the rate of change of latent heat transfer and substituting the mass with the equation valid for a homogeneous medium, which is very close to what you need.

Do you remember the definition of power? It is

$\displaystyle P = \frac{dE}{dt}$

which is the rate of change of energy transfer with time. If the power is constant over some interval $\displaystyle \Delta t$, then

$\displaystyle P = \frac{\Delta E}{\Delta t}$

and you can rearrange this to get

$\displaystyle \Delta t = \frac{\Delta E}{P}$

This is basically the idea that if you divide a total "thing" by it's constant "thing per second", you get the time taken to get the total "thing" in seconds, but applied to energy. It's no different from the solution to this: "If I buy beer at a constant rate of 2 pints per hour and I drink 8 pints, how many hours did it take?". You divide the total (8 pints) by the rate (2 pints/hour) to get the time (4 hours).

You can do the same thing for your problem question. You should consider the total latent heat transfer ($\displaystyle \Delta Q = \Delta m l = \rho \Delta V l$) and because there's no variation in the irradiance over time, you can just consider a constant heat transfer rate

$\displaystyle \dot{Q} = \frac{\Delta Q}{ \Delta t}$

(i.e. over one second) and then, once you've found the total amount of heat required to melt the ice, you just divide that total heat by the heat rate to get the time required.

 Mar 28th 2018, 05:10 AM #4 Senior Member   Join Date: Apr 2017 Posts: 392 This thread illustrates what's wrong with modern teaching methods .. Students are given to understand if only they can find the right equation or formulae for a problem , they just have to punch in the numbers , and like a calculator , the answer will come out ... no understanding of anything required ..... So they grope around for a formulae , no idea of what they're looking for ... If students were taught to think , take the problem one step at a time ,most things like this question can be solved by themselves with nothing but their own mind and reasoning powers ... And of course this approach will develop the mind and reasoning powers. topsquark likes this.
 Apr 19th 2018, 04:45 AM #5 Senior Member   Join Date: Aug 2010 Posts: 358 I am puzzled why you think "rote memorization" of formulas is a "modern teaching method". As a teaching method it goes back centuries if not millennia. And, while I am not exactly "modern" myself all of my teachers and colleagues while I was teaching avoided rote memorization. The emphasis was always on learning basic concepts and deriving formulas from them. (I will admit that the great majority of students preferred memorizing formulas to thinking!)
Apr 19th 2018, 05:13 AM   #6
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 Originally Posted by HallsofIvy I am puzzled why you think "rote memorization" of formulas is a "modern teaching method". As a teaching method it goes back centuries if not millennia. And, while I am not exactly "modern" myself all of my teachers and colleagues while I was teaching avoided rote memorization. The emphasis was always on learning basic concepts and deriving formulas from them. (I will admit that the great majority of students preferred memorizing formulas to thinking!)
Well ... you say rote memorization goes back centuries , but then say your teachers avoided it ... so you seem to confirm my point , that it's used more now ...

Certainly there has to be some equations , but I just know my mind switches off when I see lines of letters and numbers , which is more mathematics than physics .

For example this line was used on this thread to explain the melting of ice ....

"for ice melt: dQ/dt = d/dt (m x Lf) = d/dt [ (p=density) x V x lf)
(Lf = 334 KJ/kg)...."

No need !!

Such an approach only alienates the public (and many visiting this forum) and makes science elitist.

 Tags exam, ice, intensity, lake, long, melt, radiation, sunlight, time

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