# Does ice melt linearly?

I'm trying to find possible errors in this lab experiment that I did, and one question I am thinking about is "Does ice melt linearly?" I assumed that it does so in my calculations, but now I'm not so sure.

I measured the mass of melted ice (water) over a period of time and assumed that it melted at a constant rate. Since the density of ice is intrinsic (ρ = m/V) and would be constant, it made sense that the volume would change at the same rate as the mass. So that led me to believe that volume decreased at a constant rate too. Were these valid assumptions to make?

Does ice melt linearly or by some other function of time?

K^2
Short answer is no, not in general. If entire block of ice is at precisely zero degrees celcius, the rate at which it melts will be proportional to the rate at which heat flows into ice. That flow rate will depend on environment, surface area, shape, etc. If the core of the ice block is bellow zero, things get even more complex.

I know about cooling a hot object ,
Its something like of exponential curve ,
as the room temperature nears , the graphs slope becomes smaller and smaller .
Source: newtons law of cooling

Ice does not melt linearly. If you research about Newton's Law of Cooling you will find that the Temperature profile will be expressed below:

T(t) = Ta + (To - Ta)*e^(-kt)

where
Ta= ambient temperature
To= initial temperature
k= thermal conductivity
t= time

So the e expression makes it non-linear. Of course this is a very general version of the equation but it should help answer your question.

Hope this helped

russ_watters
Mentor
Newton's law of cooling does not apply here since the ice is mostly at a constant temperature. K^2 had the answer.

Well the point is that it doesn't decrease linearly whether the change in temperature is large or small, the change is non-linear.

Newton's law of cooling does not apply here since the ice is mostly at a constant temperature. K^2 had the answer.

I guess , I wrote about cooling of hot object

And melting of ice at constant temperature (0 deg) is an equilibrium state which shifts depending on the energy provided only

russ_watters
Mentor
And melting of ice at constant temperature (0 deg) is an equilibrium state which shifts depending on the energy provided only
No, it isn't/doesn't. [Pure] Ice melts at 0C, period. Increasing or decreasing the heat flux does not change that, it only changes the speed at which it melts. That's why you can use ice water as a good calibration point for a thermometer.

rcgldr
Homework Helper
Wouldn't the fact that surface area to volume (or mass) ratio increases as the size of the ice cube diminishes also be a factor?

russ_watters
Mentor
Yes, that's contained in what K^2 said, just without explaining the "surface area" part....

russ ,
you mean to say giving or taking heat doesnt shift the water and ice equilibrium .

russ_watters
Mentor
russ ,
you mean to say giving or taking heat doesnt shift the water and ice equilibrium .
Yes: Ice melts at 0C. There really isn't any "equilibrium".

K^2
That is a type of dynamic equilibrium. It's not really a static picture. With no heat flow, at 0°C you'll have simultaneous melting and fusing that balance each other out. Adding or removing heat shifts the equilibrium between phases.

Borek
Mentor
Yes: Ice melts at 0C. There really isn't any "equilibrium".

Perhaps we are using different definitions of equilibrium, then. For me an isolated mixture of ice and water at 0 deg C is a perfect example of an equilibrium - neither amount of ice nor water changes.

Actually it is an example of equilibrium given at the Newton site here. What I don't like about their explanation is that they claim there is no mass transfer between solid and liquid phase - as far as I can tell there is a mass transfer, it just goes in both directions with the same speed, so the masses of both phases don't change. Or at least that's what kinetic approach to equilibrium suggests.

Edit: K^2 posted while I was composing my post and looking for examples, and stated more or less the same.

Do ice and water exist in dynamic equilibrium ( like we study in chemistry equilibrium of ions, le chatelier principle stuff ) ?
And if heat is provided equilibrium shifts towards water side , ie more of water molecules ?

russ_watters
Mentor
I thik we might be arguing different things. I'm just talking about temperature: melting temperature is not an equilibrium, it is a constant.

Melting rate vs heat flux is an equilibrium.

Consider the other side of the coin: your house's air conditioning. If you turn it on and let it run, various competing influrnces will fight each other and eventually your house will reach an equilibrium temperature.

ok , umm
I am talking about concentration of water and ice molecules coexisting in ice water mixture , and their change in concentration when heat is provided(shifting of equilibrium) . Till no ice remains .

russ_watters
Mentor
Agreed: In a well insulated container, concentration is an equilibrium. That's pretty different from what the OP was asking though.