9. Below is a PV diagram showing a cyclic process for 0.0038 moles of an ideal monatomic gas. The direction of the cycle is shown by the arrows on the curve. The temperature does NOT change along segment ac - the process is isothermal from point a to point c. The other 2 sections of curve are graphically vertical and horizontal. (a) (b) For parts (c), (d) and (e) below, indicate whether the heat Q has gone into or out of the gas by referring to the sign, positive or negative, of your answer. (c) (d) What volume does the gas occupy at point a? What is the temperature at points a, b and c? (f) (g) (h) How much heat went into or out of the gas during segment ba? How much heat went into or out of the gas during segment cb? (e) For parts (f), (g) and (h) below, indicate whether the change in internal energy AE int negative by referring to the sign of your answer. Find the change in internal energy during segment ba. Find the change in internal energy during segment cb. Find the change in internal energy during segment ac. How much heat went into or out of the gas during segment ac? is positive or

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The image is a pressure-volume (P-V) diagram representing changes in pressure and volume of a gas system. Here's a detailed explanation:

- **Axes:**
  - The vertical axis represents pressure (P) in atmospheres (atm).
  - The horizontal axis represents volume (V) in cubic meters, scaled by \( \times 10^{-3} \).

- **Points:**
  - **Point a:** Located at a volume of 0.22 \(\times 10^{-3}\) m³ and pressure of 0.3 atm.
  - **Point b:** At the same volume as point a (0.22 \(\times 10^{-3}\) m³) but with a higher pressure of 2.2 atm.
  - **Point c:** At pressure 2.2 atm and volume not specified beyond the horizontal line.

- **Process Paths:**
  - **a to b:** A vertical arrow indicates an increase in pressure at constant volume.
  - **b to c:** A horizontal arrow shows a constant pressure process with increasing volume.
  - **c to a:** A curved arrow indicates a decrease in both pressure and volume, potentially an adiabatic or isothermal process depending on specifics not provided.

This graph is typical for thermodynamic cycles, illustrating processes such as isochoric (constant volume), isobaric (constant pressure), and potentially adiabatic/isothermal changes.
Transcribed Image Text:The image is a pressure-volume (P-V) diagram representing changes in pressure and volume of a gas system. Here's a detailed explanation: - **Axes:** - The vertical axis represents pressure (P) in atmospheres (atm). - The horizontal axis represents volume (V) in cubic meters, scaled by \( \times 10^{-3} \). - **Points:** - **Point a:** Located at a volume of 0.22 \(\times 10^{-3}\) m³ and pressure of 0.3 atm. - **Point b:** At the same volume as point a (0.22 \(\times 10^{-3}\) m³) but with a higher pressure of 2.2 atm. - **Point c:** At pressure 2.2 atm and volume not specified beyond the horizontal line. - **Process Paths:** - **a to b:** A vertical arrow indicates an increase in pressure at constant volume. - **b to c:** A horizontal arrow shows a constant pressure process with increasing volume. - **c to a:** A curved arrow indicates a decrease in both pressure and volume, potentially an adiabatic or isothermal process depending on specifics not provided. This graph is typical for thermodynamic cycles, illustrating processes such as isochoric (constant volume), isobaric (constant pressure), and potentially adiabatic/isothermal changes.
# Educational Resource: Understanding PV Diagrams

## Problem 9: Analyzing a Cyclic Process for an Ideal Monatomic Gas

Below is a PV (Pressure-Volume) diagram illustrating a cyclic process for 0.0038 moles of an **ideal monatomic gas**. The direction of the cycle is depicted by arrows on the curve. The temperature remains constant during segment **ac**, indicating an **isothermal process** from point **a** to point **c**. The other two sections of the curve are described as **graphically vertical and horizontal**.

### Questions:

(a) **What volume does the gas occupy at point a?**

(b) **What is the temperature at points a, b, and c?**

For parts (c), (d), and (e) below, indicate whether the heat \( Q \) has entered or exited the gas by referring to the sign, positive or negative, of your answer.

(c) **How much heat went into or out of the gas during segment ba?**

(d) **How much heat went into or out of the gas during segment cb?**

(e) **How much heat went into or out of the gas during segment ac?**

For parts (f), (g), and (h) below, indicate whether the change in internal energy \( \Delta E_{\text{int}} \) is positive or negative by referring to the sign of your answer.

(f) **Find the change in internal energy during segment ba.**

(g) **Find the change in internal energy during segment cb.**

(h) **Find the change in internal energy during segment ac.**

### Diagram Description:

The diagram includes a pressure-volume graph where the x-axis represents volume and the y-axis represents pressure. It has a cyclic path from point a to b to c, and back to a, with labeled segments (ba, cb, ac). Segment ac is specifically marked as isothermal, which implies constant temperature and possibly changing volume and pressure.
Transcribed Image Text:# Educational Resource: Understanding PV Diagrams ## Problem 9: Analyzing a Cyclic Process for an Ideal Monatomic Gas Below is a PV (Pressure-Volume) diagram illustrating a cyclic process for 0.0038 moles of an **ideal monatomic gas**. The direction of the cycle is depicted by arrows on the curve. The temperature remains constant during segment **ac**, indicating an **isothermal process** from point **a** to point **c**. The other two sections of the curve are described as **graphically vertical and horizontal**. ### Questions: (a) **What volume does the gas occupy at point a?** (b) **What is the temperature at points a, b, and c?** For parts (c), (d), and (e) below, indicate whether the heat \( Q \) has entered or exited the gas by referring to the sign, positive or negative, of your answer. (c) **How much heat went into or out of the gas during segment ba?** (d) **How much heat went into or out of the gas during segment cb?** (e) **How much heat went into or out of the gas during segment ac?** For parts (f), (g), and (h) below, indicate whether the change in internal energy \( \Delta E_{\text{int}} \) is positive or negative by referring to the sign of your answer. (f) **Find the change in internal energy during segment ba.** (g) **Find the change in internal energy during segment cb.** (h) **Find the change in internal energy during segment ac.** ### Diagram Description: The diagram includes a pressure-volume graph where the x-axis represents volume and the y-axis represents pressure. It has a cyclic path from point a to b to c, and back to a, with labeled segments (ba, cb, ac). Segment ac is specifically marked as isothermal, which implies constant temperature and possibly changing volume and pressure.
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