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And since water has a limited amount of thermal energy it can absorb per mass you need more mass to move more heat (without a phase change).
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How is there an upper limit? Even if you dissallow a phase change you could, in theory, rachet up the pressure as far as is needed for infinate thermal energy to pass through a given amount of water. I'm sure eventually you'd hit practical limitations in preventing a phase change, but thats beside the point.