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2.0 moles of Helium gas that initially occupies a volume of 5.0 L at a pressure of 100 kPa undergoes the following thermodynamic heat-engine cycle described below: What is the efficiency of the engine? P(kPa) 4 O a. 26% b.14% C. 10% d. 22% e. 18% 200- 100+ Q12 1 5.0 Q23 Work Q41 3 Q34 20 V(L)

2.0 moles of Helium gas that initially occupies a volume of 5.0 L at a pressure of 100 kPa undergoes the following thermodynamic heat-engine cycle described below: What is the efficiency of the engine? P(kPa) 4 O a. 26% b.14% C. 10% d. 22% e. 18% 200- 100+ Q12 1 5.0 Q23 Work Q41 3 Q34 20 V(L)

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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  1. 2.0 moles of Helium gas that initially occupies a volume of 5.0 L at a pressure of 100 kPa undergoes the following thermodynamic heat-engine cycle described below: What is the efficiency of the engine?

     

      a.

    26%
      b.

    14%
      c.

    10%
      d.

    22%
      e.

    18%
**Thermodynamic Heat-Engine Cycle Analysis** In this example, 2.0 moles of helium gas initially occupy a volume of 5.0 L at a pressure of 100 kPa. The gas undergoes a thermodynamic heat-engine cycle depicted in the pressure-volume (P-V) diagram below. The question posed is: What is the efficiency of the engine? **P-V Diagram Explanation:** - The diagram is a rectangle with points labeled 1, 2, 3, and 4 representing different states in the cycle. - The x-axis represents volume (V) in liters (L), ranging from 0 to 20 L, with significant points at 5.0 L and 20 L. - The y-axis represents pressure (P) in kilopascals (kPa), ranging from 0 to 300 kPa, with key pressure levels at 100 kPa and 200 kPa. - The cycle moves clockwise through the points: - 1 to 2 (horizontal, constant volume) - 2 to 3 (vertical, constant pressure) - 3 to 4 (horizontal, constant volume) - 4 to 1 (vertical, constant pressure) - Heat transfers are labeled for each segment: \(Q_{12}\), \(Q_{23}\), \(Q_{34}\), and \(Q_{41}\). **Efficiency Options (a-e):** Select the efficiency of the engine from the following options: - a. 26% - b. 14% - c. 10% - d. 22% - e. 18% To solve for efficiency, students would typically use the thermodynamic principles to calculate work done and heat exchange, applying the efficiency formula: \[ \text{Efficiency} = \frac{\text{Work output}}{\text{Heat input}} \times 100\% \] This diagram is an illustrative tool for understanding the mechanical work and heat transfer in a thermodynamic cycle involving an ideal gas.
Transcribed Image Text:**Thermodynamic Heat-Engine Cycle Analysis** In this example, 2.0 moles of helium gas initially occupy a volume of 5.0 L at a pressure of 100 kPa. The gas undergoes a thermodynamic heat-engine cycle depicted in the pressure-volume (P-V) diagram below. The question posed is: What is the efficiency of the engine? **P-V Diagram Explanation:** - The diagram is a rectangle with points labeled 1, 2, 3, and 4 representing different states in the cycle. - The x-axis represents volume (V) in liters (L), ranging from 0 to 20 L, with significant points at 5.0 L and 20 L. - The y-axis represents pressure (P) in kilopascals (kPa), ranging from 0 to 300 kPa, with key pressure levels at 100 kPa and 200 kPa. - The cycle moves clockwise through the points: - 1 to 2 (horizontal, constant volume) - 2 to 3 (vertical, constant pressure) - 3 to 4 (horizontal, constant volume) - 4 to 1 (vertical, constant pressure) - Heat transfers are labeled for each segment: \(Q_{12}\), \(Q_{23}\), \(Q_{34}\), and \(Q_{41}\). **Efficiency Options (a-e):** Select the efficiency of the engine from the following options: - a. 26% - b. 14% - c. 10% - d. 22% - e. 18% To solve for efficiency, students would typically use the thermodynamic principles to calculate work done and heat exchange, applying the efficiency formula: \[ \text{Efficiency} = \frac{\text{Work output}}{\text{Heat input}} \times 100\% \] This diagram is an illustrative tool for understanding the mechanical work and heat transfer in a thermodynamic cycle involving an ideal gas.
Expert Solution
Step 1

Given data :-

For helium

Moles = 2 

Initial volume = 5L

Initial pressure = 100kPa

Brief introduction:-

find the temperature at state 1,2 and 3.

Then find total heat supplied .find efficiency by dividing net work by total heat supplied.

steps

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