15-A heat engine with a diatomic gas as the working substance uses the closed cycle shown in below figure. How much work does this engine do per cycle, and what is its thermal efficiency? p (atm) 3- 0+ 3 300 K isotherm 3 - V (m³)

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**Problem 15:**

A heat engine with a diatomic gas as the working substance uses the closed cycle shown in the figure below. How much work does this engine do per cycle, and what is its thermal efficiency?

**Graph Explanation:**

The diagram presents a pressure-volume (p-V) graph with a closed cycle for a heat engine. The cycle consists of four distinct processes or stages, labeled 1 through 4, forming a rectangular loop.

- **Axes:**
  - The x-axis represents Volume (V) in cubic meters (m³), ranging from 0 to approximately 3.
  - The y-axis represents Pressure (p) in atmospheres (atm), ranging from 0 to 3.

- **Cycle Description:**
  - **Process 1 to 2:** A horizontal line indicating an isobaric expansion at a high pressure where volume increases.
  - **Process 2 to 3:** A vertical line indicating an isochoric process where volume remains constant but pressure decreases.
  - **Process 3 to 4:** A horizontal line showing isobaric compression at a low pressure where volume decreases.
  - **Process 4 to 1:** A vertical line indicating an isochoric process where volume remains constant but pressure increases.

- **Additional Elements:**
  - A dashed curve labeled "300 K isotherm" suggests that it represents a hypothetical process at a constant temperature of 300 K which provides a reference to the temperature condition of the cycle.

This cycle represents a thermodynamic process for evaluating work done and the thermal efficiency of the engine using the ideal gas law and principles of thermodynamics.
Transcribed Image Text:**Problem 15:** A heat engine with a diatomic gas as the working substance uses the closed cycle shown in the figure below. How much work does this engine do per cycle, and what is its thermal efficiency? **Graph Explanation:** The diagram presents a pressure-volume (p-V) graph with a closed cycle for a heat engine. The cycle consists of four distinct processes or stages, labeled 1 through 4, forming a rectangular loop. - **Axes:** - The x-axis represents Volume (V) in cubic meters (m³), ranging from 0 to approximately 3. - The y-axis represents Pressure (p) in atmospheres (atm), ranging from 0 to 3. - **Cycle Description:** - **Process 1 to 2:** A horizontal line indicating an isobaric expansion at a high pressure where volume increases. - **Process 2 to 3:** A vertical line indicating an isochoric process where volume remains constant but pressure decreases. - **Process 3 to 4:** A horizontal line showing isobaric compression at a low pressure where volume decreases. - **Process 4 to 1:** A vertical line indicating an isochoric process where volume remains constant but pressure increases. - **Additional Elements:** - A dashed curve labeled "300 K isotherm" suggests that it represents a hypothetical process at a constant temperature of 300 K which provides a reference to the temperature condition of the cycle. This cycle represents a thermodynamic process for evaluating work done and the thermal efficiency of the engine using the ideal gas law and principles of thermodynamics.
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