By Riemann sums, the boundary work done by a gas during an expansion process based on the information given by the statement is approximately 0.243 joules.
How to determine the boundary work done by a gas during an expansion process
A process is a consecution of states of a system. The boundary work (W), in kilojoules, is the work done by the system on surroundings and in a P-V diagram this kind of work is equal to the area below the curve, which can be approximated by Riemann sums:
[tex]W = \sum\limits_{i=1}^{n-1} p_{i}\cdot (V_{i+1}-V_{i}) + \frac{1}{2}\sum\limits_{i=1}^{n-1} (p_{i+1}-p_{i})\cdot (V_{i+1}-V_{i})[/tex] (1)
Where:
- p - Pressure, in kilopascals.
- V - Volume, in cubic meters.
[tex]W = \frac{1}{2} \sum\limits_{i=1}^{n-1} (p_{i+1}+p_{i})\cdot (V_{i+1}-V_{i})[/tex]
Now we proceed to calculate the boundary work:
W = 0.5 · [(300 kPa + 290 kPa) · (1.1 × 10⁻³ m³ - 1 × 10⁻³ m³) + (270 kPa + 290 kPa) · (1.2 × 10⁻³ m³ - 1.1 × 10⁻³ m³) + (250 kPa + 270 kPa) · (1.4 × 10⁻³ m³ - 1.2 × 10⁻³ m³) + (220 kPa + 250 kPa) · (1.7 × 10⁻³ m³ - 1.4 × 10⁻³ m³) + (200 kPa + 220 kPa) · (2 × 10⁻³ m³ - 1.7 × 10⁻³ m³)]
W = 0.243 kJ
By Riemann sums, the boundary work done by a gas during an expansion process based on the information given by the statement is approximately 0.243 joules.
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