If heat goes into a liquid, do I need to care about the work done on the liquid? Aren't they incompressible?
Sure. It's small, but when you only have solids and liquids, it is not negligible in the big picture.
(When you have a gas involved though, the work done is considerably more significant than the work done on liquids and solids at the same applied external pressure.)
The change in volume was over 15000 times as significant for a gas as for a liquid.
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Even though liquids are generally considered to be incompressible, you still need to consider the work done on the liquid when heat is added. This is because liquids can still change volume slightly in response to changes in pressure or temperature, albeit to a much smaller extent compared to gases. Additionally, the work done on a liquid may contribute to changes in its internal energy, affecting its temperature and other properties. Therefore, it's important to take into account both the heat added to the liquid and any work done on it to fully understand the changes occurring within the system.
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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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