Why do liquids contract when cooled?
temperature is a measure of kinetic energy, the lower the temperature the less motion in the liquid and the less volume.
A liquid contracts as its molecules cool down and take up less volume. The liquid contracts because the molecules' lower energy causes them to take up less space.
Water is an exception to this rule. When water cools, it expands until it reaches the freezing point, where it solidifies into a solid and forms hexagonal crystals that occupy a larger volume than the liquid.
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Liquids contract when cooled because cooling reduces the kinetic energy of the molecules, causing them to move more slowly and come closer together. This closer packing of molecules results in a decrease in the volume of the liquid, leading to contraction.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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