Assume that you have a sample of gas in a cylinder with a movable piston, as shown in the following drawing:
Redraw the apparatus to show what the sample will look like after (b) the pressure is increased from 1 atm to 2 atm at constant temperature

Verified step by step guidance

1. Identify the initial conditions of the gas: 1 atm pressure and constant temperature.
2. Understand that increasing the pressure to 2 atm while keeping the temperature constant implies a change in volume according to Boyle's Law.
3. Recall Boyle's Law: \( P_1V_1 = P_2V_2 \), where \( P \) is pressure and \( V \) is volume.
4. Since the pressure is doubled (from 1 atm to 2 atm), the volume must decrease to maintain the equation balance, assuming the amount of gas remains constant.
5. Redraw the apparatus with the piston moved inward, indicating a smaller volume of gas, while ensuring the temperature remains constant.

Key Concepts

Gas Laws

Gas laws describe the behavior of gases in relation to pressure, volume, and temperature. The most relevant laws for this question are Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. This means that if the pressure increases, the volume must decrease, provided the temperature remains unchanged.

Pressure-Volume Relationship

The pressure-volume relationship is a fundamental concept in understanding how gases behave under varying conditions. When the pressure of a gas increases, the volume decreases, as described by Boyle's Law. In this scenario, increasing the pressure from 1 atm to 2 atm will compress the gas, resulting in a smaller volume within the cylinder while maintaining the same temperature.

Constant Temperature Process

A constant temperature process, also known as an isothermal process, occurs when a gas is compressed or expanded without changing its temperature. In this case, the internal energy of the gas remains constant, and any work done on or by the gas results in a change in volume and pressure. Understanding this concept is crucial for accurately predicting how the gas will behave when the pressure is increased.