Calculate work done in a PV process
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Q.3. Find the work done using this graph.
This question includes visual content: A Cartesian coordinate system graph. The y-axis is labeled $V(m^3)$ and the x-axis is labeled $P(N/m^2)$. A straight line segment with an arrow pointing towards B starts at point A and ends at point B. Point A has coordinates $(2, 6)$ and point B has coordinates $(10, 14)$. Dashed lines connect these points to the axes at values 2 and 10 on the P-axis, and 6 and 14 on the V-axis.
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Step by Step Written Solution
Hi Mohammad, let's solve this work done problem step by step using the graph.
Reading the Graph
From the graph, point A is at pressure $2\;\text{N/m}^2$ and volume $6\;\text{m}^3$. Point B is at pressure $10\;\text{N/m}^2$ and volume $14\;\text{m}^3$.
Notice that the graph has pressure on the horizontal axis and volume on the vertical axis. For a pressure-volume graph, the work done equals the area under the curve.
Since the path from A to B is a straight line, we can use the average pressure multiplied by the change in volume.
Now let's calculate the average pressure and the change in volume.
Substitution Step
The average pressure is two plus ten over two, which gives six newtons per meter squared.
Now substitute the values into the work formula.
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