Experiment 13: Engines and Thermodynamics YOU NEED TO OBTAIN THE FOLLOWING DATA FOR PART 1 BEFORE COMING TO THE LABORATORY. If you don't, (without a legitimate excuse) the instructor will provide some typical data for you to work with and deduct 2 points from your grade. 1. Gas mileage. (Step 2 under Input Heat. ) 2. Results of road test. (Steps 1 4 under Work. ) 3. Weight of the car. (Step 5 under Work. ) Part 1: Efficiency of an Automobile You will determine the efficiency of a car. Efficiency is the ratio of the work done to the heat taken in. The heat taken in is determined from the car s gas mileage and the energy content of gasoline. The work done is found by watching the car lose speed as it coasts in neutral: The rate that the car loses energy without the engine equals the rate the engine would have to supply energy if the car was keeping a steady speed. If you don't have a car available to you, work as a partner with someone who does. Note that "efficiency," in this context, means energy out per unit of energy in, not miles driven per unit of energy in. Cars with poor gas mileage have about the same efficiency as cars with good gas mileage: Even though the engine takes in more fuel, it also does more work pulling a heavier car, giving a similar ratio. Consider a one second time interval during which your car is driven at 45 mph: Input heat (per second): 1. What is your gas mileage? (If you've never figured the gas mileage for this car, do so now if possible; otherwise, make an estimate. If you need assistance, ask the instructor.) 2. The heat of combustion of gasoline is 1.25 x 10 8 joules per gallon. This means its energy content, per gallon. Use this and your gas mileage to calculate how many joules per mile your car takes in from the fuel. (Think about canceling units to decide whether joules per gallon and miles per gallon should be multiplied or divided to get joules per mile.) 3. Convert from joules per mile to joules per second using the experiment s average speed of 45 miles per hour, and the number of seconds in an hour. (Once again, set it up by canceling units.) Work (per second): You'll want a stopwatch (you can sign one out from the lab), and your lab partners should be along to assist you and record the results. (If you want to keep stopping to record data, you can work alone.) 1. Find a section of road which is level and where you won't be a nuisance to other traffic.
2. Adjust your speed to exactly 50 miles per hour. 3. Put the car in neutral or depress the clutch so that it rolls freely, and time how long it takes to reach a speed of 40 miles per hour (making the average speed during the test 45.) Apparently, some cars can't be put in neutral while moving; in that case, do the test in drive, but you will lose speed more rapidly that way. Write "test done in drive" on your answer sheet. 4. Repeat this for a total of at least six trials, on different stretches of road, so that any out-oflevelness averages out, and average the results. 5. Record the car s weight, from the registration. Calculations: 6. Find the car's mass in kilograms from its weight using the fact that 1 kg weighs 2.21 lb. 7. Use the car's mass and initial velocity (50 mph = 22.4 meters/sec) to find its initial kinetic energy. Similarly find its final kinetic energy. (40 mph = 17.9 meters/sec.) Then, use the workenergy theorem to find the work done. (Throw away the minus sign: You just found the work done by friction, which is negative. If the car was keeping a steady speed, the engine would have to do an equal amount of positive work to counteract friction. The work done by the engine is what you actually want.) 8. Divide by the average time to obtain joules per second. Efficiency: From the heat in and corresponding work out, find your car's efficiency. Part 2: A Model Engine. Get your computer started. You will observe the work an engine does in lifting a weight, and compare to the area enclosed in its P-V diagram. The engine consists of a cylinder and piston connected by a hose to a closed metal can. A beaker of hot water is the hot reservoir; a beaker of cold water is the cold reservoir. Putting the can in the hot reservoir expands the air inside, pushing the piston up, lifting a known weight. Observing the height it is lifted tells you the work output, mgh. Putting the can in the cold reservoir contracts the air back to its original state, completing the cycle. Information for the P-V diagram comes from a pressure sensor attached to the cylinder, and from watching the piston through the transparent cylinder to obtain ΔV.
To visualize a purpose for this engine, imagine a much larger one powering an elevator. Electric motors are more practical, but it could be done this way, with each cycle lifting another passenger. Procedure: 1. Connect the can to one port at the bottom of the cylinder; connect the pressure sensor to the other. Be sure both "valves" (the plastic things that squeeze the tubing) are open. 2. Connect the sensor to channel A of the interface. Connect the interface to the computer with the USB cable and turn the interface on. Open PASCO Capstone on the computer. Click Hardware Setup at the upper left. Click the yellow circle by Channel A on the picture. Click Pressure Sensor, Low. Click Hardware Setup again. Click Two Large Digits, the third choice in the first row. In one of the displays, click <Select measurement>. On the menu that appears, select Pressure (kpa). Ignore the other display. 3. Undo one of the hose connectors to admit air, then move the piston to around the 10 mm mark. While holding up the piston, re-attach the hose. 4. Take two 1000 ml beakers to the sink and run the water until you can get a temperature under twenty in one, and a temperature in the forties in the other. Somewhere around 750 ml of water should be what fully immerses the can without overflowing the beaker. 5. Click Record. Operate the engine, recording the piston's position and the pressure at each point: Point A: The can is submerged in the cold reservoir (hold it down), no weight is on the piston. Process AB: Keeping the can in the cold water, place a 100 gram weight on the piston. This will compress the air some. Point B: Can in cold water, weight on piston. Process BC: Now, move the can to the hot reservoir. The rising temperature makes the volume expand, lifting the weight. Point C: Can in hot water, weight on piston. CD: Remove the weight, simulating the passenger getting off the elevator. The loss of this weight will allow the air to expand some. Point D: Can in hot water, no weight on piston. DA: The can could now be moved back to the cold water, to contract the air back to point A. The next passenger would then come along, and the cycle would repeat. But, you've already
got all the measurements needed to define the cycle. Calculations: 1. How much higher was the weight at point C than it was at point B? From this, calculate the potential energy gained, which is the work done on the weight. (Just the 100 g without the platform. The work done lifting the platform during BC is undone when it drops during DA.) 2. Calculate the area enclosed in the P-V diagram, shown above. The cycle is approximately a parallelogram. (AB and CD aren't really straight lines, but they're close enough.) So, the area would be the length times the width: a. The length of the parallelogram is the difference in volume between B and C. As shown at left, this is a cylindrical volume, equal to its cross sectional area times its height. To save a few minutes, this calculation has been done for you, and the results tabulated on the right. b. The width of the parallelogram is the difference in pressure between A and B. (Or, between C and D.) Note that the sensor reads in kpa, and you will need pascals. c. Calculate the area enclosed in the cycle, in joules. 3. In your conclusion, state whether the work seems to agree with the area enclosed in the P-V diagram. Assume the uncertainties in both numbers are a few percent.
Experiment 13: Engines and Thermodynamics Part 1: Input Heat: Gas mileage = Find joules per mile: Find joules per second: Work: From road test, times to coast 50 to 40 mph: average time = Weight = Mass = Calculate work done during test: Find joules per second: Calculate Efficiency:
Part 2: Piston Point position (mm) Pressure (kpa) A B C D Calculate work: Calculate length, width & area: