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Why is ice at $0^{o}$ C more effective in cooling than water at $0^{o}$ C?

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Cooling takes place when heat is removed from the system. In case of ice at $0^{o} C$ ; it will take (latent heat) from the medium to convert itself into water at $0^{o} C$ and then water at high temperature. So ice( $0^{o} C$ ) is more effective in cooling than water at $0^{o} C$ .

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