A Heat Engine: Relating Work to the P-V Cycle cylinder with trapped air piston S
ID: 1442173 • Letter: A
Question
A Heat Engine: Relating Work to the P-V Cycle
cylinder with trapped air
piston
Sound reflecting platform
canister
tubing
Figure 1: The PASCO scientific Heat Engine a.k.a. the “incredible mass lifter.”
A Real-Time Heat Engine Cycle: A canister filled with air is attached to a cylinder with a piston as shown in Figure 1. When a mass is placed on top of the piston it goes down a little bit. Then when the canister is transferred from a cold to hot water bath the piston and mass rise as the engine transforms thermal energy into mechanical work.
A Challenge: You have been studying your textbook
carefully and are trying to understand how the work done by a heat engine can be related to changes in the pressure, P, and volume, V, of its working substance.[1] In particular you would like to relate the work it takes to lift a mass to the area enclosed by a P-V diagram that describes what happens the engine’s air – its working substance.
The relationship between these factors seems weird and abstract. The goal of this assignment is explore how the work done by an engine that raises a 200 gram mass during each process of its cycles is related to the area enclosed by its P-V graph.
Figure 2: A P-V diagram for 1 cycle of the "incredible mass lifter"
Review of Types of Heat Engine Transitions:
Transition
The Working Medium Undergoes:
Isothermal
No temperature change (T is constant)
Isobaric
No pressure change (P is constant)
Adiabatic
No thermal energy transfer to or from the working medium (Q = 0)
Isovolumetric (also called Isochoric)
No volume change (V is constant)
Getting Started: Before answering the questions that follow you should open the Logger Pro file entitled with the movie inserted in it. While the movie was made, the position (y) of a sound-reflecting platform was recorded by an ultrasonic motion detector. At the same time a sensor recorded the pressure, P, in the engine’s trapped air– its working substance. The movie and the sensor data have been synchronized. If you click on the Replay button, you can examine a graph showing how y and P change during a cycle as the engine’s working substance (consisting of the air inside the canister, tubing and cylinder) expands and contracts.
1. Qualitative Considerations
(a)Four different events make the transitions in a single engine cycle happen. Using Insert>Shapes in Word, draw a line between each transition and the event that causes it. Note: These transition points are marked in Figure 2.
(b)
Transition
Cause
agb
• Mass is removed from the platform
bgc
• Chamber is moved to the hot reservoir
cgd
• Chamber is moved to the cold reservoir
dga
• Mass is placed on the platform
(c)Which type of transition (isothermal, isobaric, adiabatic or isovolumetric) describes what happens when the 200 g mass is placed on the platform so that it sinks quickly by a small amount? Explain. Hint: This process occurs in a small fraction of a second, while the air, the system’s working medium, is compressed reducing its volume and raising its temperature.
[Type answer here]
(d)Which type of transition (isothermal, isobaric, adiabatic, or isovolumetric) describes what happens when the canister is moved from the cold water bath to the hot water bath. Explain.
[Type answer here] isovolumetric
This is because the volume of the canister remains Constant only temperature and pressure changes
(e)Which type of transition (isothermal, isobaric, adiabatic, or isovolumetric) describes what happens when the 200 g mass is removed from the platform so it rises very fast? Explain. Hint: This process is very rapid and occurs in a small fraction of a second.
[Type answer here]
(f)Which type of transition (isothermal, isobaric, adiabatic, or isovolumetric) describes what happens when the canister is moved from the hot water to the cold water. Explain.
[Type answer here]
(g)For the purposes of calculating the distance through which the mass is raised after it is placed on the platform, underline and make bold, the distance, h, shown below that best represents the height through which the added 200 g mass is lifted. Explain how you arrived at your answer and show your calculation. Hint: You’ll need to use the Logger Pro Examine tool in the Analyze menu and some reasoning.
h1 = 0.033m ± 0.001m h2 = 0.039m ± 0.001m h3 = 0.044m ± 0.001m
[Type answer here]
2. Comparison of the Work Done Lifting the Mass and the Area Enclosed by the P-V Curve
(a)Use W = mgh to determine the work done by the engine on the mass while it is being lifted: Calculate the work done on the mass by the engine from its location just after it is placed on the platform to the maximum height it rises to during the single engine cycle. Show your calculations with appropriate standard international units (meters, kilograms, seconds) included with your numbers.
[Type answer here]
(b)Determine the area enclosed by the P-V graph in Joules: For your convenience, we have created a new calculated column in Logger Pro to determine V – the total volume of the engine’s working medium. We used geometrical calculations and position data to do this calculation. On Page 2 of the Logger Pro file (entitled ), we created a graph of the air pressure in the engine as a function of the total volume, V, of the air trapped in the engine (including the canister, hose and cylinder).
If you remember your geometry, you’ll recognize that the area enclosed by the graph in Figure 3 is simply the area of a parallelogram of height h and base b (as shown in Figure 3). In this case h represents the magnitude the change in pressure as the mass is put on the platform (or taken off of it) and b represents the change in volume of air in the engine’s cylinder as the air expands when warmed (or contracts when cooled).
Figure 3: P-V graph for 1 engine cycle
Calculate the area enclosed by the P-V diagram. Show your calculations with units. Hints: Careful use of appropriate SI (MKS) units is essential. The pressure unit of kPa represents a kilopascal. It is equal to 1000 pascals where a pascal is 1 N/m2.
[Type answer here]
3. Reflections on Your Findings
How did the values for useful work compare to each other? Does it seem reasonable to state that the area enclosed by a P-V graph has the same value as the direct calculation of the mechanical work done by the heat engine as it lifts a mass? Please compare your two calculations and calculate that percent difference between your results.
[Type answer here]
[1] All heat engines use a working substance that can expand or contract as it exchanges energy with its surroundings. In our PASCO engine the working substance is the air trapped in a cylinder, hose, and canister.
cylinder with trapped air
piston
Sound reflecting platform
canister
tubing
Figure 1: The PASCO scientific Heat Engine a.k.a. the “incredible mass lifter.”
A Real-Time Heat Engine Cycle: A canister filled with air is attached to a cylinder with a piston as shown in Figure 1. When a mass is placed on top of the piston it goes down a little bit. Then when the canister is transferred from a cold to hot water bath the piston and mass rise as the engine transforms thermal energy into mechanical work.
A Challenge: You have been studying your textbook
carefully and are trying to understand how the work done by a heat engine can be related to changes in the pressure, P, and volume, V, of its working substance.[1] In particular you would like to relate the work it takes to lift a mass to the area enclosed by a P-V diagram that describes what happens the engine’s air – its working substance.
The relationship between these factors seems weird and abstract. The goal of this assignment is explore how the work done by an engine that raises a 200 gram mass during each process of its cycles is related to the area enclosed by its P-V graph.
Figure 2: A P-V diagram for 1 cycle of the "incredible mass lifter"
Explanation / Answer
(c) Which type of transition (isothermal, isobaric, adiabatic or isovolumetric) describes what happens when the 200 g mass is placed on the platform so that it sinks quickly by a small amount?
Adiabatic process due to the short fractin of time.
(d) Which type of transition (isothermal, isobaric, adiabatic, or isovolumetric) describes what happens when the canister is moved from the cold water bath to the hot water bath.
Isovolumetric. This is because the volume of the canister remains constant only temperature and pressure changes.
(e) Which type of transition (isothermal, isobaric, adiabatic, or isovolumetric) describes what happens when the 200 g mass is removed from the platform so it rises very fast?
Isovolumetric as volume remains constant.
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