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The relationship between pressure and volume of a gas is so that as volume decreases, pressure

Question

The relationship between pressure and volume of a gas is

so that as volume decreases, pressure

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Solution

The relationship between pressure and volume of a gas is described by Boyle's Law, which states that for a given mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. This can be mathematically represented as:

P1VorPV=k P \propto \frac{1}{V} \quad \text{or} \quad PV = k

where P P is the pressure, V V is the volume, and k k is a constant. This means that if the volume of the gas decreases, the pressure increases, provided the temperature remains constant.

For example, if you compress a gas into a smaller container (thus decreasing its volume), the molecules of the gas will collide with the walls of the container more frequently, leading to an increase in pressure. Conversely, if the volume increases, the pressure decreases.

In conclusion, Boyle's Law illustrates that there is a direct inverse relationship between the pressure and volume of a gas under isothermal conditions. As one quantity decreases, the other must increase to maintain the relationship.

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