Lab 4 Heat Engine Objective The objective of this lab is to build a heat engine, to operate it, and to measure its efficiency. ackground Here is the heat engine we are building. rotary motion sensor to computer work mass 100 g piston piston mass 35 g hot reservoir cold reservoir low pressure sensor to computer boiling water ice water air can This engine runs between two temperature reservoirs, ice water (a few degrees ) and almost boiling water (almost 100 ). The heat exchange occurs through the aluminum air can. The work is done on a mass placed on the piston. This cycle should be repeatable if no leak occurs. We will measure two things. The height of the piston (and thus the volume of the air) using the rotary motion sensor and the pressure of the air using the low pressure sensor. There are only two temperatures in this cycle. The initial volume of the air is important. This includes the can, tubing, and the volume under the piston. The initial pressure is due to the atmosphere and the piston. The mass of the piston and the diameter of the piston are on the piston label. page 1
Procedures: DataStudio Setup Launch DataStudio. onnect both the rotary motion sensor and the low pressure sensor to DataStudio. Select both sensors. Set their sampling rates to 10 Hz. For the rotary motion sensor, de-select the angular position checkbox. Select the second measurements tab and check the position measurement only. In the Rotary Motion Sensor tab, set the resolution to high and set the linear scale to large pulley (groove). We are using the large pulley on the sensor whose circumference is 15 cm. There is no calibration necessary for this. Loop the string over the rotary motion sensor such that when the volume of the air increases, the displacement is positive. Run the string around the pulley in the opposite direction if the displacement is negative. Test it out. For the low pressure sensor, select the pressure measurement. The calibration values are preset. Note that the base value for the pressure sensor is zero when exposed to the atmosphere. Procedures: The Engine Here are the steps for running the engine. (1) Set up the Initial State. State Un-attach the pressure sensor so that air can flow in and out. Lock the piston into place at 2 cm mark above the base using the lock screw. Do not place the work mass in the piston yet. Place the air can into the ice water. Wait for the air to cool. Give it about 5 minutes. ttach the air can to the pressure sensor. Release the piston. Wait for the piston to come to rest. Once in equilibrium, the state of the air should not change. Start the data recording. The temperature is ice water temperature. Measure and record it. T = T ice water The pressure is due to the atmosphere plus the weight of the piston. P = P atm + m piston g piston The volume is due to the air can, the tubing, and the piston height. V = V can +V tubing +V piston You can now calculate the number of moles of air inside the can. Make sure the units work out and that the results are reasonable. n = P V RT page 2
(2) Put the Mass onto the Piston. Process (5 seconds) Place the 100 gram work mass onto the piston. Let it sink. The pressure increases. The volume decreases. The temperature does not change since it is in contact with the cold reservoir. work in heat out isotherm The temperature is still the ice water temperature. T = T The pressure is increased by the weight of the 100 gram mass. P = P + The volume is decreased by the piston height. (3) Heat up the ir. Process (10 seconds) (0.1 kg)g piston V = V Δx piston Place the can into the boiling water. This is where the heat goes in and the work is done to raise the 100 gram mass. work out heat in isobar The temperature is now the boiling water temperature. T = T boiling water The pressure is mostly constant along the process. P = P The volume is V = V + Δx piston page 3
(4) Remove the Mass. Process D (5 seconds) Take the work mass off of the piston. Let the air expand further. Work is done by the air, but this is not useful work since the work mass is off the piston. isotherm work out heat in The temperature is still the boiling water temperature. T D = T boiling water The pressure drops back down to the level of state due to the atmosphere and the piston. P D = P The volume is V D = V + Δx D piston (5) Place the ir an ack into the Ice Water. Process D (10 seconds) We are returning the air back to the initial state. This is where excess heat is removed. The final state is state again. isobar work in heat out D page 4
nalysis Model the cycles as two isobars ( and D) and two linear processes ( and D). We can assume that the isotherms are linear since they are short. Identify the state variables (P,V, and T) for the four states. The pressures and D should be averages across each process. alculate the work and heat for all processes using the above states. Use the molar specific heat at constant pressure for air of 29 J/mol K. onclusion alculate the real efficiency of this engine. The real efficiency uses the actual useful work done. This is raising the 100 gram mass by the height change. The work done on the piston does not count. Post Lab eff = W done on mass Q total input What is the theoretical maximum efficiency that can operate between the two temperature reservoirs in this lab? What is the theoretical efficiency of this cycle (two isotherms and two isobars)? ase the limits on your measured temperatures and pressures. The work done is the area of the PV diagram of the cycle. page 5