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? (c) Decrease the volume by 45% at constant T

Verified step by step guidance

1. Step 1: Understand the problem. We are asked to determine the effect on the gas pressure inside a cylinder if the volume is decreased by 45% at a constant temperature.
2. Step 2: Recall the ideal gas law, which states that the pressure of a gas is directly proportional to its temperature and inversely proportional to its volume, assuming the amount of gas is constant. This can be expressed as PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
3. Step 3: Since the temperature and the amount of gas are constant in this problem, we can simplify the ideal gas law to P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.
4. Step 4: If the volume is decreased by 45%, this means that the final volume V2 is 55% of the initial volume V1. Therefore, we can express V2 as 0.55V1.
5. Step 5: Substitute V2 into the simplified ideal gas law equation. Since P1V1 = P2V2, and V2 = 0.55V1, we can write the equation as P1V1 = P2(0.55V1). From this equation, we can see that if the volume decreases, the pressure must increase to maintain the equality. Therefore, decreasing the volume by 45% at constant temperature will increase the gas pressure inside the cylinder.

Key Concepts

Gas Laws

Gas laws describe the relationships between pressure, volume, and temperature of gases. The most relevant here is Boyle's Law, which states that at constant temperature, the pressure of a gas is inversely proportional to its volume. This means that if the volume decreases, the pressure must increase, provided the temperature remains constant.

Pressure

Pressure is defined as the force exerted per unit area. In the context of gases, it results from the collisions of gas molecules with the walls of their container. When the volume of a gas is reduced, the molecules have less space to move, leading to more frequent collisions and thus an increase in pressure.

Volume and Temperature Relationship

The relationship between volume and temperature is governed by Charles's Law, which states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature. However, in this scenario, since the temperature is held constant while the volume decreases, we focus on Boyle's Law to understand the pressure change.