Q15PE - College Physics (Urone)

Question

What is the net work output of a heat engine that follows path ABDA in the figure above, with a straight line from B to D? Why is the work output less than for path ABCDA? Explicitly show how you follow the steps in the Problem-Solving Strategies for Thermodynamics.

Step-by-Step Solution

Answer

The net work output of a heat engine that follows the path ABDA is 2400 J . The smaller value is due to the smaller area under the curve ABD.

Step 1: Analyze the figure and find an expression to calculate the net work output.

The figure is a PV diagram. That means the graph of pressure verses volume. So, the area the curve in the PV diagram will give the net work output. Therefore, you need to calculate the area of  ∆𝐴𝐵𝐷$∆ABD$.

The area of a triangle is equal to the half of the product of its base and height.

Here,  b is the base and h is the height of the triangle.

Step 2: Calculate the area of triangle ABD.

The base and height of the triangle corresponds to the change in pressure and the change in volume, respectively.

Therefore, the net work output of heat engine that follows the path ABDA is  2400 J.

Step 3: Explain why the work output along path ABDA is less than that of path ABCDA.

Since the area under the graph gives net work output, the area under the curve will have a larger net work output. Here, the net work output along the path ABCDA is equal to the area of the quadrilateral ABCD.

Therefore, the net work output along ABCDA is larger, because of the area contribution of  ∆𝐵𝐶𝐷  along with  ∆𝐴𝐵𝐷  while in the path ABDA, only area of  ∆𝐴𝐵𝐷 contributes to the total area.

So, the area under the curve of 𝐴𝐵𝐷𝐴  is smaller than that of ABCDA , which results in a smaller work output.