Heating substances in paper cups?

[Cheesycheese213]

In class, we briefly discussed those experiments where a paper cup is filled with water and heated, and the cup does not end up burning while the water is able to boil.

From what I remember of what was said, although I am not sure I understood correctly, the water has a much higher specific heat capacity (4.18 J) than the paper (around 1.34 J) and so the heat energy would transfer from the cup to the water and prevent it from reaching the temperature needed? Websites etc. generally explain it similarly, although they also talk about the difference in temperatures to boil (100°C)/ignite (around 230°C?).

I was wondering what would happen if a fluid with a similarly high heat capacity but a higher maximum temperature(?) than the paper was used? Would the cup eventually still catch on fire once the fluid passes ~230°C?

Thanks!

 

[sophiecentaur]

Summary:: (Boiling water in paper cups)

once the fluid passes ~230°C?

The water would have boiled away before that.

 

[Nugatory]

I was wondering what would happen if a fluid with a similarly high heat capacity but a higher maximum temperature(?) than the paper was used? Would the cup eventually still catch on fire once the fluid passes ~230°C?

By “maximum temperature” you mean “boiling point”?

If so, yes, the cup will catch on fire or do whatever other exciting thing it does when it is overheated.

 

[russ_watters]

In class, we briefly discussed those experiments where a paper cup is filled with water and heated...

Heated how? If you apply a direct flame to the paper, I would expect it to burn through. In a microwave the temperature is just the temperature of the water. Either way, heat capacity has nothing to do with whether it burns, that I can see.

 

[256bits]

Heated how? If you apply a direct flame to the paper, I would expect it to burn through. In a microwave the temperature is just the temperature of the water. Either way, heat capacity has nothing to do with whether it burns, that I can see.

good point - I agree - more factors are at play than just the specific heat of water.

Thermal diffusivity, which is the ratio of the thermal conductivity to the specific heat capacity and density, of the water might be a better reason why the paper does not burn.

In a substance with high thermal diffusivity, heat moves rapidly through it because the substance conducts heat quickly relative to its volumetric heat capacity or 'thermal bulk'. <-- sentence from wiki

How quickly the water can keep the paper "cool" would also depend not just upon the water, but also upon the rate of heat application and thermal properties of the paper. With a high temp concentrated flame at one spot on the paper, there could be local boiling of the water and rapid temperature increase of the paper spot to the point that it burns through.

Usually, though, something in contact with water will not burn wholeheartedly, if at all, until the water has all boiled away, as the side with the water will be globally kept at 100C while there is still liquid water in contact with the surface. Once all the liquid water has turned to steam, which by the way has a better thermal diffusivity than liquid water by a factor of 23.38 / 0.143, ( meaning that the temperature variation of the steam is more quickly evened out, at least in the vicinity of the heated surface ), the temperature of the heated surface can increase rapidly, due to the now low thermal mass next to the heated surface.

Stacking several paper cups inside one another, filling the interior one with water, and blow torching the ensemble would give a different outcome ( charring and burning of the outer cups before the water boils away ), does question the suggestion that only the specific heat of water is the determining factor here.