Thermal capacity and enthalpies of fusion and vaporization.

Thermal capacity and enthalpies of fusion and vaporization. Sept 12, 2021 5:11:19 GMT -5 nei, Benfxmth, and 1 more like this

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Post by Babu on Sept 12, 2021 5:11:19 GMT -5

I studied some simple physics last year and barely put in any effort whatsoever into those studies. Most things we were taught, apart from the practical aspects of doing the calculations, weren't really news to me, and few things actually surprised me.

The one thing that probably surpised me, and amazed me, the most, was the absolutely insane amounts of energy needed to melt and evaporate water. For example, it takes the same amount of energy to turn H2O from -0.01°C to 0.01°C as it takes to turn it from 0.01°C to about 80°C.

And if you have a 1kg block of -10°C ice, you only need 9g of water vapor to warm the entire block of ice to 0°C. That last part is absolutely insane and really gives a ton of insight into what goes into snow melting.

For example, if you want to melt 10kg of snow (0°C), you can either condense 1.5 kg of water vapor, or you can use the thermal conduction of 120 000 liters of 23°C air. So basically, if you put a 10kg snowpile in a closed container that's 2.5m tall (standard ceiling height) and 6.9x6.9m, so basically a 516sqft/48m² apartment (and it's a theoretical closed container), eventually the temperature of the entire apartment is gonna cool down to 0°C (if we assume a constant dew point of 0°C). But if the 23°C air is at a 100% RH, the room would only have to be 1.9x1.9m large, or 39sqft/3.6m² to melt the entire snow block using ONLY condensation (i.e. without even factoring in the temperature and thermal capacity of the air). And this is using the realistic pretense that the air stops condensing once the dew point drops to 0°C (if we instead assumed that every molecule of water in the air would condense, only a 1.65x1.65m room would be required).

These are calculations about the volume/mass/energy needed for melting snow and don't say anything about the actual melting speed. I don't really know how quickly water vapor is able to condense, compared to how quickly air can thermally conduct its heat, and so I don't know for sure how much humidity actually affects the speed of snow-melt. However, amount-wise, the actual temperature of the air becomes very insignificant compared to the humidity of the air (23°C air has 13x more melting capacity at 100% humidity than with a 0°C dew point)

Edit: Shit, I realize I forgot a zero. The water vapor condensation needed to melt the 10kg ice block/snow pile would be equivalent to a 36m² apartment (2.5m ceiling), not 3.6m². So while 23'C saturated air still has more "melting energy" from the water vapor than the air's thermal capacity, it's not as drastic as I originally calculated.

Thermal capacity and enthalpies of fusion and vaporization. Sept 12, 2021 8:31:09 GMT -5 Benfxmth likes this

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Post by Babu on Sept 12, 2021 8:31:09 GMT -5

I conducted an experiment to see how much condensation mattered when melting ice. I put an ice cube on a rust iron coil (just to hold the ice cube in place; a mesh would've been optimal but I don't have that) on top of a leather-insulated shot glass. The idea is that as the ice cube melts the water drops down into the shot glass, and because the shot glass is isolated enough, there will neither form condensation on the glass nor the water inside the glass, and it won't affect the melting rate of the ice cube in any way either. The most major source of potential error is the conductive (and possibly condensation-forming) properties of the iron coil interfering with the melting of the ice cube.

I weighed the setup with a resolution of 0.01g (I'm also assuming a ±0.01g precision) before and after the cube had melted. The cube itself weighed 7.17g and can be assumed to be -10°C initially, which means 2527J is needed to melt the cube. This equates to the energy released by the condensation of 1.12g of water vapor. Dividing the post-melted weight gain by this number will give the factor that condensation played in the melting process (a 0.66 g increase in weight would mean 50% of the melting occured due to condensation).

A thermometer was placed next to the rig and measured 21.7°C @ 54.3% RH and a dew point of 12.2°C. The 12.2°C dew point means that there was an additional 5.95g of water vapor per m³ compared to if the dewpoint were to be 0°C. 21.7°C air has approximately 46kJ more energy than 0°C air per m³. Since 5.95g of water vapor stores 13.4kJ, that means the water vapor accounts for 22.7% of the volumetric "melting capacity" of the air.

The results of my experiment was as follows: The ice cube melted in 50 minutes and the weight increased by 0.16g. This means condensation accounted for 14.3% of the energy needed to melt the cube, which is less than what would be expected if thermal convection and condensation had energy transfer rates proportional to their respective shares of the total thermal energy potential, which would indicate that heat energy in air transfers via condensation at only 0.46x the rate of thermal convection. So if the total thermal capacity in a m³ of air was split 50/50 between water vapor and air temperature, approximately 31.5% of the energy transfer would be due to condensation of water vapor, and 68.5% would be due to regular thermal convection.
This ultimately contradicts my hypthesis which was that the energy transfer rate would either be proportional, or if anything skewed so that condensation would play an even bigger role relative to its share of the total thermal capacity. It is however possible that most of this discrepancy is due to the iron coil, since most of the coil probably would've stayed above, or very near, the 12'C dew point, and thus not induced condensation, whereas all of it would've helped conduct heat to the ice cube from the air, thus increasing the effect that the actual air temperature had on the melting of the ice.

Images of the setup before and after melting the ice cube had melted: