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fleetfootmikeYou have an ice cube, 1m on a side, frozen in the centre of which is a 20cm x 4cm metal statuette. It's removed from a cooler at -3 deg C, and placed on a wooden pedestal, 1m square in vertical cross section, in the middle of an air conditioned shopping mall at 17 deg C.
How long does the ice cube take to melt completely?
It's relatively easy to work out how much energy you need to melt the ice, using the specific heat capacity of ice to work out how much you need to get it from -3 to 0 deg C, and then the latent heat of fusion to figure out how much you need to melt it.
Trickier is how long it takes for that amount of energy to flow in. The equation I suspect I need to apply is Q/t = kA(T1 - T2)/l, where
Q = heat energy transferred
t = time
k = conductivity of material
A = area
T1, T2 = temperature at either end
l = distance
We can assume a shell of air around the cube on 5 of its six sides, of some thickness we can only guess at, temperature 17deg C at one side, 0C at the other, and apply the above in some handwavy manner (and ditto for the wood table). However, as time goes by, the cube melts and A shrinks, and I spy some very handwavy guesswork and some integration going on.
Anyone any thoughts?
How long does the ice cube take to melt completely?
It's relatively easy to work out how much energy you need to melt the ice, using the specific heat capacity of ice to work out how much you need to get it from -3 to 0 deg C, and then the latent heat of fusion to figure out how much you need to melt it.
Trickier is how long it takes for that amount of energy to flow in. The equation I suspect I need to apply is Q/t = kA(T1 - T2)/l, where
Q = heat energy transferred
t = time
k = conductivity of material
A = area
T1, T2 = temperature at either end
l = distance
We can assume a shell of air around the cube on 5 of its six sides, of some thickness we can only guess at, temperature 17deg C at one side, 0C at the other, and apply the above in some handwavy manner (and ditto for the wood table). However, as time goes by, the cube melts and A shrinks, and I spy some very handwavy guesswork and some integration going on.
Anyone any thoughts?
