Since holidays are upon us, and to break free from holiday spirit, I find myself driving to a coffee shop. While their upper level is often almost empty, it's an unspoken obligation of If your cup is empty, you better order something more ... so that you can sit more; made me wonder, "What kind of cup should I get my coffee into, from the ones available over the counter, so that I can sit at this coffee shop the longest?". The answer was quite simple - anything that's got a lid on top. Whether that's your takeaway cup or repurposing table coasters as lid (don't do that!) on porcelain house cup at given coffee shop or cafe that served your coffee in. That answers one half of the question - qualitatively speaking. But the more important question that needs to be addressed, "How can I ensure that my coffee stays warm the longest?"

For brevity, I'm not gonna dive into full blown physics. In an ideal world, but this equation should suffice to understand what goes behind-the-scenes to understand. Let me spit out tl;dr right away before you have other important nuances in life to attend to,

So how did I arrive to this conclusion? By some primitive testing,
⤷ Test 1: Lid Heat Retention Test On Two Identical Porcelain Cups
Boiling hot water was poured in two identical porcelain cups. Left cup is covered by saucer (cup brim was sealed even when it looks tapered), and the right cup was covered by run-of-the-mill paper napkin.

When both cups were filled and covered with lids, notice how both body and lid of left-side cup was hotter at touch than cup on right side. One might think that cup on right i.e. one with paper napkin is dissipating lesser heat to the surrounding and thus would stay even more warmer, right? Well, thanks to bi-material composition i.e. two different material types between cup's body and lid, cup on right side, even though being less warmer to touch, dissipates heat much faster. The end result - while body and lid of left cup is warmer at touch, somehow it retains heat from within, due to uniformity in inner surface composition. Hence I kept cup with hotter water within the GIF, while cup with relatively less hot water got kicked out,

TL;DR of Test 1 : Using lid of same material as cup body retains heat longer
Now that we know to use lid of same material as cup body, time to pit two cup offerings usually offered by baristas at coffee shop - togo (or takeaway) cup vs porcelain cup
⤷ Test 2: ToGo (or Takeaway) Paper vs Porcelain Cup
Had to bring home my cup from this other coffee shop, instead of tossing out in trash. After letting these two cups sit still for 15 minutes, I checked to see which one was even more warmer,
⤷ And we have a winner - the ToGo (or Takeaway) cup!
How did that ToGo or Takeaway cup emerge out to be a winner? The answer lies in body structure of these cups. These cups are air insulated, double walled in architecture.


⤷ Internal Structure of ToGo/Takeaway Cup
The Polyethylene (PE) liner inside somehow blocks liquid from otherwise being soaked by porosity of paper walls. Now that I think about it, everyday use of ToGo or Takeaway cup can be detrimental for health, for the risk of ingesting micro-plastics with every sip of coffee from such cups.
I tried modeling such a composite cup structure, until I found heat transfer function for such composite materials in Department Of Energy documentation for nuclear reactors; something to do with cooling (if my memory serves right from few weeks ago, perhaps; something that I found late in middle of night and saved it as a web clipping in my lab journal).
⤷ Heat Transfer Function Of Composite Material - Ref. 1
⤷ Heat Transfer Function Of Composite Material - Ref. 2 (alternate source; somewhere online)
One of the other things that also mattered is ratio of cup's wall surface area, to the volume of beverage that's filled within. The empty space inside cup, determines how much vapor from beverage gets trapped in that air gap, and further dictates vaporization rate in that space, followed by convection through side-walls and lid on top. Starbucks advertises their Short, Tall and Grande drinks to be 8, 12, and 16 ounces in serving size respectively. But it took me a trip to local Starbucks outlet to get an approximate cup dimensions, and postulate that cup_surface_area/volume metric.

Based on these amateur observations, calculations, half-baked experiments and inferences, I can say one thing: get a Tall sized drink in a takeaway cup and don't forget to ask Barista for a stopper, if you really wanna sit at a coffee shop for extended time and have your hot beverage last hot ... the longest.