Compare the amount of work on the gas required for ideal gas processes A, B, &C (in diagram at right). The inequalities incorporate correct sign. Processes A, B, & C have the same initial state and the same final state.

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### Comparing Work on Ideal Gas Processes

In the study of thermodynamics, it's important to understand the work done on a gas during different processes. Here, we examine the work required for ideal gas processes A, B, and C using the provided Pressure—Volume (PV) diagram.

#### Process Overview
- **Initial State:**
  - Pressure (P) = 1000 Pa
  - Volume (V) = 0.10 m³
- **Final State:**
  - Pressure (P) = 250 Pa
  - Volume (V) = 0.40 m³

#### Graph Analysis
The provided diagram shows the PV curves for three different processes (A, B, and C) that transition between the same initial and final states:

- **Process A:** A vertical path from the initial pressure of 1000 Pa to 250 Pa at constant volume (0.10 m³), followed by a horizontal path where the volume increases from 0.10 m³ to 0.40 m³ at constant pressure (250 Pa).
- **Process B:** A diagonal path showing a linear decrease in pressure from 1000 Pa to 250 Pa while the volume increases from 0.10 m³ to 0.40 m³.
- **Process C:** A horizontal path where the volume increases from 0.10 m³ to 0.40 m³ at constant pressure (1000 Pa), followed by a vertical path where the pressure decreases from 1000 Pa to 250 Pa at constant volume (0.40 m³).

#### Work Done on Gas
The work done on the gas is represented by the area under the PV curve. This can be summarized as:

- **Process A:** Since process A involves vertical and horizontal steps, the work done can be computed directly by the areas of the respective rectangles.
- **Process B:** This forms a trapezoid under the PV curve, so the work done is the area of that trapezoid.
- **Process C:** Similar to Process A but the order of volume and pressure changes are reversed.

### Multiple-Choice Question
Based on the PV diagram, compare the work done (with the correct sign incorporation) for processes A, B, and C:
1. A = B = C
2. A = B > C
3. A = C > B
4. A > B > C
5. C > B > A
Transcribed Image Text:### Comparing Work on Ideal Gas Processes In the study of thermodynamics, it's important to understand the work done on a gas during different processes. Here, we examine the work required for ideal gas processes A, B, and C using the provided Pressure—Volume (PV) diagram. #### Process Overview - **Initial State:** - Pressure (P) = 1000 Pa - Volume (V) = 0.10 m³ - **Final State:** - Pressure (P) = 250 Pa - Volume (V) = 0.40 m³ #### Graph Analysis The provided diagram shows the PV curves for three different processes (A, B, and C) that transition between the same initial and final states: - **Process A:** A vertical path from the initial pressure of 1000 Pa to 250 Pa at constant volume (0.10 m³), followed by a horizontal path where the volume increases from 0.10 m³ to 0.40 m³ at constant pressure (250 Pa). - **Process B:** A diagonal path showing a linear decrease in pressure from 1000 Pa to 250 Pa while the volume increases from 0.10 m³ to 0.40 m³. - **Process C:** A horizontal path where the volume increases from 0.10 m³ to 0.40 m³ at constant pressure (1000 Pa), followed by a vertical path where the pressure decreases from 1000 Pa to 250 Pa at constant volume (0.40 m³). #### Work Done on Gas The work done on the gas is represented by the area under the PV curve. This can be summarized as: - **Process A:** Since process A involves vertical and horizontal steps, the work done can be computed directly by the areas of the respective rectangles. - **Process B:** This forms a trapezoid under the PV curve, so the work done is the area of that trapezoid. - **Process C:** Similar to Process A but the order of volume and pressure changes are reversed. ### Multiple-Choice Question Based on the PV diagram, compare the work done (with the correct sign incorporation) for processes A, B, and C: 1. A = B = C 2. A = B > C 3. A = C > B 4. A > B > C 5. C > B > A
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