My five-year-old wants to know whether ice cream or an ice lollipop (aka a popsicle) melts faster. Does the dairy content in ice cream make it melt more slowly or more quickly?
Update: Assume constant mass and surface area to volume ratio
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10$\begingroup$ I'm thinking you (and your five year old) need to perform a very extensive experimental program. Just be careful to not waste any of the treats. I suggest sitting in your back yard on pleasant summer evenings as the proper place for the experiments. $\endgroup$– Jon CusterJul 21, 2021 at 14:44
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1$\begingroup$ Melting time depends on not just the food, but also the portion size. A larger portion has lower surface area to volume ratio, so takes longer to melt. Comparison to a lolly is even trickier, as this ratio also depends on shape. $\endgroup$– J.G.Jul 21, 2021 at 15:15
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2$\begingroup$ Is mass being kept constant? Or volume? Because icecream is full of air. But it's pretty difficult to beat water in terms of specific heat capacity. The popsicle likely wins out simply because it has more water in it. $\endgroup$– DKNguyenJul 21, 2021 at 15:55
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$\begingroup$ What an absolutely perfect way to introduce your child to the wonders of scientific experimentation. $\endgroup$– foolishmuseJul 21, 2021 at 16:27
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2 Answers
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The ice cream melts faster. That is because there is milk in ice cream, while there is water in a popsicle. There is ice coating on the popsicle, while there is none on the ice cream, therefore making the ice cream melt faster than the popsible.
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Let’s assume constant mass and constant surface area, rather than constant surface-area-to-volume ratio. (Although, the density difference would probably not have been the main factor even if we had simply assumed same shape and volume.)
So, we have the same area exposed. And the same mass. Maybe slightly different shapes.
What matters now is the melting point, the “coefficient of conduction” (how well that material conducts heat, ie how much heat transfers through the matter at a given temperature difference), and the “thermal heat capacity” (how much heat energy it takes to heat-up a unit of mass by one degree). The thermal heat capacity tells us how much heat must be absorbed by the environment to make the necessary temperature increase. Technically we also have the amount of heat needed to transition from liquid to solid at the melting point - this means once the matter is at the melting temperature, it takes heat just to make the phase transition. But those will be nearly identical. I’d also imagine the melting points are very similar or identical, leaving the other two factors. This is generally true for nonionic mixtures in water; so for example it wouldn’t apply to salt, which does significantly change melting point. So it’s down to thermal heat capacity and coefficient of conduction.
The popsicle conducts heat better because of the lack of binding and milk solids, meaning it has a higher coefficient of conduction. This factor tends to make the popsicle melt faster due to the fact that it will absorb heat from the surroundings faster (and that in turn is true because it will more quickly bring heat to its center from the surface and hence keep the surface cooler and hence more able to accept heat from the warmer air - a cooler surface means a bigger temperature difference between surface and air which means faster absorption of heat, because temperature difference drives heat transfer in a directly proportional manner, no temp difference no heat transfer, high temp difference high heat transfer, etc).
I’m guessing the popsicle also has a lower thermal heat capacity and hence will require less absorbed heat per degree increase, but I’m not certain it does. If so, that also tends to make the popsicle melt faster.
Our intuition says the ice cream will melt faster because it softens with temperature, but thats not the problem being considered. It is time to total melting, to liquid. But this softening brings up another factor I just thought of. If the ice-cream softens and changes shape then it could begin to flatten and increase its exposed surface area. That could be a big factor. Id suggest doing the experiment with identical shapes unconstrained to allow for this factor of softening ice-cream to flatten as it goes and increase area and hence melting AND doing the experiment eliminating this factor by putting them in identical cups. The difference might alter which of the two melts faster. For the cups it will, counterintuitively, be the popsicle that becomes all liquid first. For the blobs, it will probably be the ice-cream because the flattening as it softens will increase surface area so much that any differences in thermal material properties will not be enough to overcome the faster absorption of heat.
