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 (c) the temperature is decreased from 300 K to 200 K and the pressure is decreased from 3 atm to 2 atm.

Verified step by step guidance

1. Identify the initial conditions of the gas sample, which are a temperature of 300 K and a pressure of 3 atm.
2. Note the final conditions that the gas sample needs to reach, which are a temperature of 200 K and a pressure of 2 atm.
3. Understand that according to the combined gas law, which is expressed as \(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\), where P is pressure, V is volume, and T is temperature, a decrease in both temperature and pressure will affect the volume of the gas.
4. Since both the temperature and the pressure of the gas are decreasing, the volume of the gas will also decrease. This is because the decrease in temperature tends to decrease the kinetic energy of the gas molecules, leading to a decrease in volume, and the decrease in pressure allows the gas to occupy less space.
5. Redraw the apparatus showing the piston at a lower position than initially, indicating a decrease in the volume of the gas. The space above the piston in the cylinder should be smaller, reflecting the combined effect of reduced temperature and pressure.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law helps predict how a gas will behave under changing conditions, making it essential for understanding the effects of temperature and pressure on gas samples.

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 concept is crucial for predicting how the volume of the gas in the cylinder will change as the temperature decreases from 300 K to 200 K.

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 principle is important for understanding how the pressure change from 3 atm to 2 atm will affect the volume of the gas in the cylinder, especially when combined with the temperature change.