Assume that you have a cylinder with a movable piston. What would happen to the gas volume of the cylinder if you were to do the following? (c) Decrease the pressure by 75% at constant T?

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Identify the relationship between pressure and volume for a gas at constant temperature. This is described by Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. Mathematically, this is expressed as:

P V_{1} = P_{2} V_{2}

Understand the problem statement: You are asked to decrease the pressure by 75%. This means the new pressure,

P_{2}

, is 25% of the original pressure,

P_{1}

. Therefore,

P_{2} = 0.25 P_{1}

Substitute the new pressure into Boyle's Law equation:

P V_{1} = 0.25 P_{1} V_{2}

Solve for the new volume,

V_{2}

, by dividing both sides of the equation by

0.25 P_{1}

V_{2} = rac{P V_{1}}{0.25 P_{1}}

Interpret the result: Since the pressure is decreased by 75%, the volume of the gas will increase. Specifically, the volume will become four times the original volume, as the pressure is reduced to one-fourth of its original value.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law, represented as PV = nRT, relates the pressure (P), volume (V), and temperature (T) of an ideal gas. It indicates that for a given amount of gas at constant temperature, the product of pressure and volume is constant. This law is fundamental in understanding how changes in pressure affect gas volume.

Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature is held constant. This means that if the pressure decreases, the volume must increase, provided the temperature remains unchanged. This principle is crucial for predicting the behavior of gases in response to pressure changes.

Gas Behavior at Constant Temperature

When analyzing gas behavior at constant temperature, it is important to recognize that temperature affects the kinetic energy of gas molecules. At constant temperature, any decrease in pressure will lead to an increase in volume, as the gas molecules will spread out to occupy a larger space. This relationship is essential for understanding the dynamics of gases in a piston-cylinder system.

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Assume that you have a cylinder with a movable piston. What would happen to the gas pressure inside the cylinder if you were to do the following? (b) Reduce the amount of gas by one-third while holding the temperature and volume constant

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