Can matter undergo phase transitions?
...If it is matter, then I hope so. If it is matter, it should be describable by a phase diagram (at least, in principle).
Benzene is a fine example:
- If we start at
#"280 K"# and#"30 torr"# , and increase the pressure at constant temperature past roughly#"40 torr"# ......We condense the gas into a liquid. (If we reverse the process we just did, we vaporize the liquid into a gas.)
- If we start at
#"273 K"# and#"10 torr"# , and increase the pressure at constant temperature, we move vertically upwards in the phase diagram.We consequently transform the gas into a solid, i.e. deposition, past roughly
#"30 torr"# . (If we reverse the process, we perform sublimation.)- And if we look closely, the solid-liquid coexistence curve has a negative slope (is not perfectly vertical).
So if we start at roughly
#"280 K"# and#"40 torr"# (to the left of the triple point) and increase the pressure at constant temperature, past roughly#"50 torr"# we would melt the solid into a liquid. (The reverse process would be freezing the liquid.)
- And if we look closely, the solid-liquid coexistence curve has a negative slope (is not perfectly vertical).
- If we start at
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Phase transitions can occur when a substance undergoes changes in temperature or pressure, causing it to change from one phase (solid, liquid, or gas) to another. Some examples of phase transitions include sublimation (solid to gas), melting (solid to liquid), freezing (liquid to solid), vaporization (liquid to gas), condensation (gas to liquid), and deposition (solid to solid). Yes, matter is capable of undergoing phase transitions.
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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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