When do real gases behave most like ideal gases?

Answer 1

Under low temperatures and high pressures, gases behave less like ideal gases and more like real gases.

Qualities of an ideal gas include the following:

#1# The particles are extremely tiny compared to the volume filled by the gas - like mathematical points.
#2# The particles are very far apart and moving fast.
#3# The particles have no features (shape) and exert no forces on each other other than by collision.

Most gases approximate this well when the temperature is high enough to cause the particles to move quickly and when the pressure is low enough to cause the particles to be small and far apart relative to the gas volume.

When the pressure is increased, the number of particles in the same volume increases, so the volume of the particles becomes a bigger proportion of the volume of the gas. When the pressure is high enough, we can no longer assume that qualities #1# and #2# above are the case.
When the temperature decreases the particles move more slowly, which makes the part of quality #2# about moving fast invalid, and as they move slower they are more likely to exert electrical forces on each other, making quality #3# invalid.
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Answer 2

Real gases behave most like ideal gases under conditions of high temperature and low pressure.

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Answer from HIX Tutor

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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