I know it's a manga about dragons but I still wonder where all this ice is coming from. Is she sucking out the moisture from the surrounding air? Using her own body's water supply? I feel like that would dehydrate her incredibly quickly so maybe a mixture of both? The answer is probably 'dragon magic' but I'm still curious about the deeper physical implications of these powers.
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I thought about the moisture in the air myself, but in the end opted out for the 'dragon magic' as you more aptly defined it.
Rarely do authors think about these kind of things.
The big ice spike on her head looks like roughly 1 kg of ice.
With the values for water content in the air from this table: at 30 °C (since the chapter is in summer) with roughly 30 g/m³, that would mean roughly 30 m³ at full water saturation would be needed to make this one ice shard.
Which is possible considering the class room has probably something like (6x10x3 = 180 m³) as volume. But the picture at end with the buckets full of ice are most likely dragon magic or they would have needed to cool down and dehumify enough air to probably change the local weather.