Question

thermodynamics

Answer 1

The thickness of ice in a lake is 5cm and the temperature of ait is -10 degree celsius .calculate time required for thickness of ice to be doubled .Take latent heat of ice =80 cal/g
density of ice =.92 g/cc
and conductivity of ice =0.004 cal cm^-1s^-1 degree celsius^-1

Answer 2

I do not know what kind of solution is expected here. I give this problem to my students almost every year, and it is like a 4-page answer with complicated differential equations. I cannot see any easy way how to simplify it.

Is it supposed to be a long problem for you?

- I think you have to assume that the temperature of the top layer of ice is equal to -10°C (not true in reality).

- Temperature at the boundary between ice and water is freezing temperature 0°C.

- Equations for steady-state are valid, with quantities varying very slowly with time.

Answer 3

Do you know the answer? If find about 19 hours.

Answer 4

i dont hav the answer with me

Answer 5

You must work out the infinitesimal heat necessary to freeze an elementary dl thickness of water (assume surface is S).

Work out the heat transfer across the ice in elementary time dt.

Assume steady-state and equate both expressions. You will end up with a DE between l and t that you can integrate between thickness e and 2e.

Answer 6

hmm.. this seems pretty "long" as u mentioned

Answer 7

I don't know what is expected :-(

You can assume a mean heat transfer for thickness = 7.5 cm and us it throughout. That might do it.
I will try and tell you what I find.

Answer 8

k

Answer 9

*use

Answer 10

lemme look what othrs hav to say @shivam_bhalla , @Mani_Jha , @EarthCitizen , @TuringTest

Answer 11

@experimentX

Answer 12

@ujjwal , @apoorvk

Answer 13

It works ! Assuming mean heat transfer is that for 7.5 cm yields the same result 69000 s :-))

Answer 14

hmm can u pls show the wrking?

Answer 15

@Vincent-Lyon.Fr , I think the water beneath the ice sheet is converted to ice on top, Am I right?? If yes, then the what should we assume the temperature of water to be ??

Answer 16

Water must be 0°C, if not ice would melt!

Answer 17

Great. The process would be

\[Q = Q_{0^o \to 0^oC}{(water ->ice)}+Q_{0^o \to -10^oC}{(ice ->ice)}\]
\[Q_{0^o \to 0^oC}{(water ->ice)}= mL = (density)(volume)L\]
\[Q_{0^o \to -10^oC}{(ice ->ice)}= mc(\Delta)T = (density)(volume)c(-10 -0)\]

Answer 18

@Vincent-Lyon.Fr , Please verify the equations I have written above

Answer 19

It looks like this where z = 0 is taken on top of ice-sheet.
You have to use Fourier's law to work out power escaping topwards through ice.