The Second Law of Thermodynamics Lab Reading Assignment: Fundamentals of Physics, Halliday, Resnick and Walker Ed 8, Chapter 20 Summary of relevant concepts: Thermodynamic processes can be categorized as reversible and irreversible. We define a state function S called “entropy” that forms the basis of the Second Law of Thermodynamics. The change in entropy for a reversible process can be calculated using the equation: f dQ Sif T i The change in entropy for an irreversible process can be computed by connecting the initial and final states via a reversible path and calculating the change in entropy as above. The Second Law of Thermodynamics states that the entropy of a closed system either stays the same or increases – it can never decrease. The Second Law of Thermodynamics also sets a fundamental limit on the efficiency of a heat engine. The most efficient theoretically possible is the Carnot engine with an efficiency: TL C 1 TH Heat Engines & Entropy In the reading assignment and in lecture, we have already learnt about the ideal Carnot engine that is based upon a particular cycle of processes. Engines can however be built upon many different types of cycles. For instance, the gasoline internal combustion engine depends upon a cycle that consists of adiabatic and isochoric expansion/compression steps. In this discussion activity, we will use the “Stirling cycle” to illustrate the concepts of heat engine efficiency and entropy in a heat engine. This is a fascinating engine invented by Robert Stirling in 1816. Your instructor will have demonstrated a Stirling engine in lecture and there may be a working model for examination in the lab. You can learn more about the technology of Stirling engines at the following website: http://www.stirlingengine.com/faq A reversible Stirling heat engine uses 0.001 moles of He gas and works by extracting and dumping heat between two reservoirs at 127 0C and 27 0C. The gas starts out in a state with temperature 127 0C and with a volume of 1 cm3. It then is taken to states B, C, and D via the following cycle: Process AB: an isothermal expansion at 127 °C from 1 cm3 to 2 cm3; Process BC: an isochoric cooling to 27 °C; Process CD: an isothermal compression at 27 °C back to 1 cm3; and Process DA: an isochoric heating back to the initial conditions. Questions: Q1. Draw the four steps of the Stirling cycle on a p-V diagram. Be sure to label the axes, the directions of each of the steps and the temperatures of any isotherms. Q2. Determine the work done by the engine WAB, the heat absorbed by the engine QAB, and the change in entropy ΔSAB of the engine in the isothermal expansion (process AB). Clearly explain all the steps in your calculation. Q3. Repeat the calculation in Q.2 for all the steps in the Stirling cycle and fill in the following table. (You should append a couple of pages showing your detailed work at the end of the lab report.) W (J) Q (J) ΔS (J/K) Process AB Process BC Process CD Process DA Complete cycle Q4. Use your results from Q2-3 to determine the efficiency of this engine. How does this compare with the efficiency of a Carnot engine working between the same two heat reservoirs? Q5. If you really built an engine with these specifications, would you expect the efficiency of the engine to have the efficiency that you calculated? Explain your answer briefly – you should incorporate the concepts of reversibility and irreversibility in your discussion. Q6. In the table that you completed earlier, are there any processes during which the entropy of the Stirling engine decreases? If so, is this a violation of the Second Law of Thermodynamics? Explain your answer with a detailed discussion of all the changes in entropy during one cycle of the Stirling engine.
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