Heat Engine

Introduction

In this experiment you will lift a mass using the expansion of a heated gas, as shown in Figure 1. The mass is on a platform that is lifted by a graphite piston. The piston moves with very little friction within a hollow cylinder (Figure 2). The cylinder is attached to an air chamber through a small flexible tube. As the air temperature inside the air chamber increases, its volume will increase forcing more air into the cylinder, and thus into the cylinder, raising the platform. If the air temperature in the air chamber decreases, its volume will decrease drawing air from the cylinder and tube and lowering the platform.

Figure 1: Doing useful mechanical work by lifting a mass, m, through a height, y

You will compute mechanical work, net thermodynamic work, and net heat transfer. To then return the piston to the resting position, your system must undergo an entire thermodynamic cycle (Figure 3). You can compute the mechanical work the system does by determining the distance through which the mass was lifted and the force required to do so. By carefully noting the pressure and volume at each point in the cycle, you can also compute the thermodynamic work required to complete the cycle. In addition, by knowing the temperature of the air and the changes in pressure or volume it undergoes, you can compute the change in entropy that the gas undergoes and the resulting heat transfer associated with it.

While the system does have a constant pressure throughout, the temperature in the cylinder and air chamber is not necessarily the same. Because of the narrow size and long length of the tube, it takes a great deal of time before the air chamber and cylinder temperatures can equilibrate. Thus, it is probably a good approximation to consider the air chamber and cylinder to be separate systems as far as temperature and heat transfer, but a single system when considering the expansion or contraction of the air inside.

Figure 2: Experimental Setup for heat engine

Figure 3 Thermodynamic Work in a heat engine cycle

Results and Discussion

  1. Using your initial pressure measurement, the measurement of room temperature, and the volume of the air chamber compute the mass of air in the air chamber.
  2. For each of the nine experimental runs, calculate the volume and the pressure after each of the four stages and generate P-V curves. You can assume that air is an ideal gas.
  3. From your P-V data, compute the net thermodynamic work for the cycle. Compute the mean and Standard Deviation of the net work.
  4. For each of the nine experimental runs and assuming the air chamber temperature is the same as the ice water and boiling water, compute the entropy in the air chamber and generate T-S curves for the cycle. Because you have no measure of the absolute entropy, assume minimum entropy value of the cycle corresponds to zero entropy.
  5. From your T-S data, compute the heat into the system from the high temperature reservoir and net heat transfer for the cycle. Compute the mean and Standard Deviation of the net heat transfer.
  6. Compare the net work and net heat transfer. Which one is greater? Should they be equal? Is the change in entropy of the air chamber the same as the change in entropy of the whole system?
  7. Compute the thermodynamic efficiency of the device. What kind of efficiency did you expect?
  8. Compute the mechanical work done by the device. How does it compare to the thermodynamic work?
  9. What are the sources of error in this lab? How do they affect the measurements and computations?

Why do the different runs have different values of net work and net heat transfer? What do the statistics tell you about how repeatable the experiment is and how reliable the results are?

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