You have a gas at 25 C confined to a cylinder with a movable piston. Which of the following actions would double the gas pressure? (a) Lifting up on the piston to double the volume while keeping the temperature constant (b) Heating the gas so that its temperature rises from 25 C to 50 C, while keeping the volume constant (c) Pushing down on the piston to halve the volume while keeping the temperature constant.

Verified step by step guidance

1. Identify the initial conditions of the gas: constant temperature at 25°C and a certain volume.
2. Recall the ideal gas law: \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature in Kelvin.
3. Convert the given temperature from Celsius to Kelvin: \( T(K) = 25 + 273.15 \).
4. Analyze each option: (a) Doubling the volume while keeping temperature constant will halve the pressure, according to Boyle's Law (\( P_1V_1 = P_2V_2 \)). (b) Doubling the temperature in Kelvin will double the pressure if volume is constant, according to Gay-Lussac's Law (\( \frac{P_1}{T_1} = \frac{P_2}{T_2} \)). (c) Halving the volume while keeping temperature constant will double the pressure, according to Boyle's Law.
5. Determine which action results in doubling the pressure: Option (c) is correct, as halving the volume while keeping temperature constant will double the pressure.

Key Concepts

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 shows that for a given amount of gas (n) at a constant temperature, pressure is inversely proportional to volume. This means that if the volume decreases, the pressure increases, assuming temperature remains constant.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. This means that increasing the temperature of a gas will increase its volume, which can affect the pressure if the volume is not allowed to change. Understanding this law helps in analyzing how temperature changes impact gas behavior.

Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. This means that if the volume of a gas is halved, the pressure will double, provided the temperature does not change. This principle is crucial for understanding how compressing a gas affects its pressure.