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How is pressure related to kinetic energy?

Answer 1

William Audy

For an ideal gas, the relation is given by
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Given the following ideal gas relation
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Answer 2

Axel Acevedo

Pressure is related to kinetic energy through the kinetic theory of gases, which states that the pressure exerted by a gas is proportional to the average kinetic energy of its molecules. Specifically, pressure ( P ) is directly proportional to the kinetic energy per unit volume ( \frac{1}{2}mv^2 ) and the number of gas molecules ( n ), and inversely proportional to the volume ( V ) of the container:

[ P = \frac{1}{3} n \cdot \frac{1}{2}mv^2 ]

This equation shows that an increase in the kinetic energy of gas molecules leads to an increase in pressure, assuming the number of molecules and the volume remain constant. Conversely, a decrease in kinetic energy results in a decrease in pressure. Therefore, there is a direct relationship between pressure and kinetic energy in gases.

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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.