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3. (II) Sketch a PV diagram of the following process: 2.5 L of ideal gas at atmospheric pressure is cooled at constant pressure to a volume of 1.0 L, and then expanded isother- mally back to 2.5 L, whereupon the pressure is increased at constant volume until the original pressure is reached.

3. (II) Sketch a PV diagram of the following process: 2.5 L of ideal gas at atmospheric pressure is cooled at constant pressure to a volume of 1.0 L, and then expanded isother- mally back to 2.5 L, whereupon the pressure is increased at constant volume until the original pressure is reached.

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College Physics
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Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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**Problem 3: PV Diagram Sketch** Sketch a \( PV \) diagram of the following process: 2.5 L of ideal gas at atmospheric pressure is cooled at constant pressure to a volume of 1.0 L, and then expanded isothermally back to 2.5 L, whereupon the pressure is increased at constant volume until the original pressure is reached. ### Detailed Explanation: 1. **Starting Condition:** - Initial Volume (\( V_i \)): 2.5 L - Initial Pressure (\( P_i \)): Atmospheric pressure 2. **Cooling at Constant Pressure:** - The gas is cooled at constant pressure. - The volume decreases from 2.5 L to 1.0 L. - On the \( PV \) diagram, this is represented as a horizontal line from (2.5 L, \( P_i \)) to (1.0 L, \( P_i \)). 3. **Isothermal Expansion:** - The gas is then expanded isothermally, meaning at constant temperature. - The volume increases back to 2.5 L. - Since it's isothermal, the pressure decreases as the volume increases according to Boyle's Law (\( PV = \text{constant} \)). - On the \( PV \) diagram, this appears as a curved line from (1.0 L, \( P_i \)) to (2.5 L, lower pressure). 4. **Increasing Pressure at Constant Volume:** - Finally, the pressure is increased back to the original pressure at constant volume. - The volume remains at 2.5 L while the pressure increases back to \( P_i \). - On the \( PV \) diagram, this is represented as a vertical line from (2.5 L, lower pressure) to (2.5 L, \( P_i \)). ### Graphical Representation: A PV diagram generally plots Pressure (P) on the y-axis and Volume (V) on the x-axis. - The horizontal line represents the constant pressure cooling process. - The isothermal process appears as a curve, reflecting the inverse relationship between pressure and volume. - The vertical line indicates the process of increasing pressure at constant volume.
Transcribed Image Text:**Problem 3: PV Diagram Sketch** Sketch a \( PV \) diagram of the following process: 2.5 L of ideal gas at atmospheric pressure is cooled at constant pressure to a volume of 1.0 L, and then expanded isothermally back to 2.5 L, whereupon the pressure is increased at constant volume until the original pressure is reached. ### Detailed Explanation: 1. **Starting Condition:** - Initial Volume (\( V_i \)): 2.5 L - Initial Pressure (\( P_i \)): Atmospheric pressure 2. **Cooling at Constant Pressure:** - The gas is cooled at constant pressure. - The volume decreases from 2.5 L to 1.0 L. - On the \( PV \) diagram, this is represented as a horizontal line from (2.5 L, \( P_i \)) to (1.0 L, \( P_i \)). 3. **Isothermal Expansion:** - The gas is then expanded isothermally, meaning at constant temperature. - The volume increases back to 2.5 L. - Since it's isothermal, the pressure decreases as the volume increases according to Boyle's Law (\( PV = \text{constant} \)). - On the \( PV \) diagram, this appears as a curved line from (1.0 L, \( P_i \)) to (2.5 L, lower pressure). 4. **Increasing Pressure at Constant Volume:** - Finally, the pressure is increased back to the original pressure at constant volume. - The volume remains at 2.5 L while the pressure increases back to \( P_i \). - On the \( PV \) diagram, this is represented as a vertical line from (2.5 L, lower pressure) to (2.5 L, \( P_i \)). ### Graphical Representation: A PV diagram generally plots Pressure (P) on the y-axis and Volume (V) on the x-axis. - The horizontal line represents the constant pressure cooling process. - The isothermal process appears as a curve, reflecting the inverse relationship between pressure and volume. - The vertical line indicates the process of increasing pressure at constant volume.
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