How does temperature affect the kinetic energy in gases, liquids, and solids?
Temperature affects the kinetic energy in a gas the most, followed by a comparable liquid, and then a comparable solid.
The higher the temperature, the higher the average kinetic energy, but the magnitude of this difference depends on the amount of motion intrinsically present within these phases.
IN GASES In general, the average kinetic energy increases at higher temperatures for gases. Since gases are quite compressible, the effects of higher or lower temperature are significant.
IN LIQUIDS For liquids and solids, it is much simpler. Since liquids have intermolecular forces binding them together, temperature really only affects the strength of those intermolecular forces, since those forces are restricting the effects of the change in average kinetic energy. As temperature increases, the average kinetic energy of the liquid molecules increases until the intermolecular forces break. You won't often see noticeable changes in the volume or looseness of the liquid, since they are fairly incompressible. When the intermolecular forces break and we get to the boiling point, that's when you can have more freely-moving particles, but even then, anything still in the liquid form is still fairly incompressible. IN SOLIDS For solids, the rigid nature of the lattices the particles are in restricts their kinetic energy from affecting much of the average motion in the solid. As temperature increases, the average kinetic energy increases, but we will see hardly any obvious difference in volume or shape. When we approach the melting point, the lattice energies break and allow the particles to move slightly more freely, but still leaving them fairly incompressible. For solids, temperature changes, in the absence of induced phase changes, usually just manifests itself as temperature changes, and nothing else.
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Increasing temperature raises kinetic energy in gases by enhancing molecular motion. In liquids, higher temperature boosts molecular motion and weakens intermolecular forces. In solids, elevated temperature augments vibrational motion of particles within the fixed structure.
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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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