Use the Trapezoidal rule to compute the work done in KJ. Work is given by = [ Pav PdV W = Pressure (kPa) | 336 294.4 266.4 260.8 260.5 249.6 193.6 165.6 Volume (m³) 0.5 2 3 4 6 8 10 11
Use the Trapezoidal rule to compute the work done in KJ. Work is given by = [ Pav PdV W = Pressure (kPa) | 336 294.4 266.4 260.8 260.5 249.6 193.6 165.6 Volume (m³) 0.5 2 3 4 6 8 10 11
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Instruction: Compute Work Using the Trapezoidal Rule**
To compute the work done, in kilojoules (KJ), apply the Trapezoidal Rule. Work is given by the integral:
\[ W = \int P \, dV \]
**Data Table:**
Below is the table of Pressure (P) and Volume (V) values:
| Pressure (kPa) | 336 | 294.4 | 266.4 | 260.8 | 260.5 | 249.6 | 193.6 | 165.6 |
|----------------|-------|-------|-------|-------|-------|-------|-------|-------|
| Volume (m³) | 0.5 | 2 | 3 | 4 | 6 | 8 | 10 | 11 |
**Explanation:**
- **Columns:**
- The first row lists pressure values in kilopascals (kPa).
- The second row lists corresponding volume values in cubic meters (m³).
- **Trapezoidal Rule Application:**
- This numerical method approximates the integral of the pressure-volume data.
- Calculate the area under the curve formed by the Pressure vs. Volume using trapezoids, where each pair of consecutive points defines a trapezoid.
Compute the work by summing the areas of these trapezoids to get the total work done in kilojoules.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20ef5b89-bdf5-4ebf-bc1c-34f412b810c9%2F5fef2c99-ae82-4baf-8847-e1314f860610%2Fp9mher_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction: Compute Work Using the Trapezoidal Rule**
To compute the work done, in kilojoules (KJ), apply the Trapezoidal Rule. Work is given by the integral:
\[ W = \int P \, dV \]
**Data Table:**
Below is the table of Pressure (P) and Volume (V) values:
| Pressure (kPa) | 336 | 294.4 | 266.4 | 260.8 | 260.5 | 249.6 | 193.6 | 165.6 |
|----------------|-------|-------|-------|-------|-------|-------|-------|-------|
| Volume (m³) | 0.5 | 2 | 3 | 4 | 6 | 8 | 10 | 11 |
**Explanation:**
- **Columns:**
- The first row lists pressure values in kilopascals (kPa).
- The second row lists corresponding volume values in cubic meters (m³).
- **Trapezoidal Rule Application:**
- This numerical method approximates the integral of the pressure-volume data.
- Calculate the area under the curve formed by the Pressure vs. Volume using trapezoids, where each pair of consecutive points defines a trapezoid.
Compute the work by summing the areas of these trapezoids to get the total work done in kilojoules.
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