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# 9.2: Activities

## Things You Will Need

Nothing! All the data you need is provided.

## A PV Diagram in Real Time

The video below shows side-by-side the cycle of the engine (broken down in terms of processes) and the PV diagram the cycle generates. Actually the "PV diagram" plots the pressure of the trapped air versus the position of the piston, not the volume of the air. But all of the changes in volume occur within the glass cylinder shown, which means that volume changes can be computed from piston displacements by multiplying by the cross-sectional area of the cylinder.

[You might notice a small weight attached to a string that is attached to the piston and hangs over a pulley. While it seems like this might have an effect on the experiment, it actually does not, because this hanging weight (like the piston and the platform it supports) remain involved for the complete cycle. Their changes in height do involve changes in gravitational potential energy, but as gravity is a conservative force, there is no work put into or taken out of the system by these objects over a complete cycle. The purpose of that small weight is to keep tension in the string so that the pulley will turn. The pulley is connected to the computer, and the amount it turns is converted into the displacement of the piston for the computer output.]

The full engine cycle is broken down into four videos below, each labeled according to the PV diagram given in the Background Material. Before jumping into the data analysis that follows, see if you can reconcile the physical action in the video with the PV diagram that mirrors it in real time.

## Data Analysis

For the analysis that follows, here are some needed measurements:

• mass of weight that is lifted by the piston = $$200g$$
• cross-sectional area of piston = $$8.3\times 10^{-4}m^2$$

And of course we have the full PV diagram, which we saw at the end of the last process video. It may be that you need to clearly determine where a specific process begins, and where it ends, which may be difficult to ascertain from this diagram, so you should be prepared to go back to the videos for this information.

1. Let's start by checking to see if the work output of the engine as depicted on the PV diagram reasonably matches the work performed raising the weight.
1. Estimate the work output of the engine. Explain how you are making this estimate.
2. Determine the work done raising the weight. Note that you will need to use the height change of the weight from the moment it is placed on the piston to the moment it is removed.
3. How do the two values above compare? Unless they are precisely equal, one is larger than the other. Does it make sense that this one should come out slightly larger? Why?
2. Now for the somewhat more challenging task of computing this engine's thermal efficiency. For this number, we need the work output (which we have already in 1a above) and the heat added to the gas by the hot thermal reservoir.
1. During which segment(s) of the engine's cycle ( ($$a$$) – ($$h$$) ) does the gas receive heat from the hot reservoir?
2. Use the fact that air is basically a diatomic ideal gas to compute the heat received by the gas from the hot reservoir.
3. Compute the engine's thermal efficiency, and compare it to the maximum possible efficiency of an engine driven by these same two reservoirs.

## Lab Report

Download, print, and complete this document, then upload your lab report to Canvas. [If you don't have a printer, then two other options are to edit the pdf directly on a computer, or create a facsimile of the lab report format by hand.]