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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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**Exercise 3: Creating a PV Diagram** In this exercise, we will sketch a Pressure-Volume (PV) diagram for the following process of an ideal gas: 1. Start with 2.5 liters (L) of ideal gas at atmospheric pressure and cool it at constant pressure until the volume reduces to 1.0 L. 2. Next, expand the gas isothermally back to a volume of 2.5 L. 3. Finally, increase the pressure at constant volume until the original pressure is attained. ### Step-by-Step Explanation: #### Step 1: Isobaric Cooling - **Initial State:** 2.5 L of ideal gas at atmospheric pressure. - **Process:** Cool the gas at constant pressure. - **Final State:** Volume reduces to 1.0 L at the same pressure. On the PV diagram, this process is represented by a horizontal line moving leftward from 2.5 L to 1.0 L at constant pressure. #### Step 2: Isothermal Expansion - **Initial State:** Gas at 1.0 L after being cooled. - **Process:** Expand the gas isothermally (constant temperature). - **Final State:** Volume expands from 1.0 L back to 2.5 L. On the PV diagram, this process is depicted by a curve (since PV is constant for an isothermal process) moving rightward, returning to the original volume of 2.5 L. #### Step 3: Isochoric Pressure Increase - **Initial State:** Gas at 2.5 L after isothermal expansion. - **Process:** Increase the pressure while keeping the volume constant. - **Final State:** Pressure increases to its original value. On the PV diagram, this process is shown by a vertical line moving upward, indicating an increase in pressure while the volume remains at 2.5 L. ### Diagram Description: After following these steps, the resulting PV diagram should show: 1. A horizontal line from 2.5 L to 1.0 L. 2. A curved line from 1.0 L back to 2.5 L. 3. A vertical line upward at 2.5 L to the original pressure level. This diagram visually represents the changes in pressure and volume throughout the described process for an ideal gas.
Transcribed Image Text:**Exercise 3: Creating a PV Diagram** In this exercise, we will sketch a Pressure-Volume (PV) diagram for the following process of an ideal gas: 1. Start with 2.5 liters (L) of ideal gas at atmospheric pressure and cool it at constant pressure until the volume reduces to 1.0 L. 2. Next, expand the gas isothermally back to a volume of 2.5 L. 3. Finally, increase the pressure at constant volume until the original pressure is attained. ### Step-by-Step Explanation: #### Step 1: Isobaric Cooling - **Initial State:** 2.5 L of ideal gas at atmospheric pressure. - **Process:** Cool the gas at constant pressure. - **Final State:** Volume reduces to 1.0 L at the same pressure. On the PV diagram, this process is represented by a horizontal line moving leftward from 2.5 L to 1.0 L at constant pressure. #### Step 2: Isothermal Expansion - **Initial State:** Gas at 1.0 L after being cooled. - **Process:** Expand the gas isothermally (constant temperature). - **Final State:** Volume expands from 1.0 L back to 2.5 L. On the PV diagram, this process is depicted by a curve (since PV is constant for an isothermal process) moving rightward, returning to the original volume of 2.5 L. #### Step 3: Isochoric Pressure Increase - **Initial State:** Gas at 2.5 L after isothermal expansion. - **Process:** Increase the pressure while keeping the volume constant. - **Final State:** Pressure increases to its original value. On the PV diagram, this process is shown by a vertical line moving upward, indicating an increase in pressure while the volume remains at 2.5 L. ### Diagram Description: After following these steps, the resulting PV diagram should show: 1. A horizontal line from 2.5 L to 1.0 L. 2. A curved line from 1.0 L back to 2.5 L. 3. A vertical line upward at 2.5 L to the original pressure level. This diagram visually represents the changes in pressure and volume throughout the described process for an ideal gas.
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