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Heat Engine Purpose In this lab you will investigate the operation of a simple heat engine used to lift a mass, You will measure the work done by the heat engine by plotting a PV diagram and calculating the area. You will then compare that value of the work to the mechanical work. Procedure For this procedure you will be measuring pressure and volume at the points a, b, c, and d in the following PV diagram. The work done by the heat engine is the area of the parallelogram. V The diagram for the heat engine is shown below. The heat engine is a small cylinder with a Attach Pressure Gauge Cold Hot diameter of 32.5 mm. A piston can move up and down and a mass can be placed on the tray at the top of the piston. A pressure gauge is attached to the heat engine as well as a small metal cylinder, The small metal cylinder will be moved between the cold water bath and hot water bath. Changes in the volume of the gas can be observed directly by the markings on the piston chamber. The markings show the distance up the cylinder in mm. The volume is TRZh, where R is the radius of the cylinder and h is the distance up the cylinder. Use meters so that the volume is in m'.The different stages of the heat engine are described below and in the figure below. Starting with position a, the air chamber is in the ice bath and no mass is on the platform. Add 100 grams to the platform. The pressure will increase due to the extra mass and the volume will go down. This is position b on the PV diagram. Put the air chamber in the hot bath. The pressure is constant (why?) and the volume increases. This is position c on the PV diagram. Remove the mass from the platform. The pressure will decrease, and the volume will increase. This is position d on the PV diagram. Putting the air chamber in the cold bath should return to position a on the PV diagram. Point A Point B Point C Point D Cold Cold Hot Hot The table below gives the actual data as measured in the lab by a former lab group. Position Height (mm) Pressure (kPa) A 20 100.93 B 16 102.07 C 45 102.11 D 46 100.93 1. Plot the PV diagram. Use Pascals for pressure and cubic meters for volume. Plot using an xy-scatter plot with the option to connect the dots. To close the shape, include position A as both the first and last value, that is, plot pressure and volume for A, B, C, D, and A. 2. Calculate the area inside the "parallelogram." The graph is not a perfect parallelogram, but there are various ways to calculate the area. a. If you have taken Calculus III, there there is a way using the cross product to get the area. I will not try to explain this process, but if you are familiar with this techniquethen feel free to use it. b. The side ab is the most off. The other three sides are reasonably close to a parallelogram. You can get a good approximation to the area by imagining a new line that goes through the midpoint of line ab and is parallel to the y-axis. The new line will make the distance be shorter, and the distance ad longer. Line cd will be unchanged. You will then have a pretty good parallelogram whose area is the base times the height. The base is the change in volume from either postion d to the new postion a or from position c to the new position b. The height is the change in pressure from postions c to d, or from the new position a to the new position b. 3. Calculate the mechanical work done by lifting the mass. The height that the mass is lifted should be the difference between points c and b of the heat engine cycle. Compare this to the work from the PV diagram. Calculate the percent difference. | Measurement, - Measurement2| Percent Difference = x 100 (Measurement, + Measurement2)