Lab
A Sample Heat Engine
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Equipment
The equipment which will be used in this lab is: the PASCO Gas Law Apparatus, a ring stand, an ice-water bath, a hot water bath, a stainless-steel temperature probe, a gas-pressure sensor, LabPro interface, a 100 gram mass, and various tube couplings.
The PASCO heat engine apparatus is a closed system consisting of a nearly friction-free piston inside a cylinder. It has two air tubes leading from the cylinder: one going to a pressure sensor (which is measured using the Lab Pro) and the other leading to an air reservoir (aluminum can) that we will immerse in water to change the temperature of the air in the system. There is also be a temperature probe connected to the interface to record the temperature of each water bath.
The manufacturer states that the piston has a diameter of 32.5 ± 0.1 mm and a mass of 35.0 ± 0.06 grams.
The platform on the top of the piston gives you the ability to add a mass that will change the pressure in the cylinder. The manufacturer recommends that this mass does not exceed 200 grams; we will use a 100-gram slotted mass. The pressure sensor measures the absolute pressure in the cylinder, P, in kPa.
As the piston moves, the volume of the cylinder changes, The total volume of the air in the system consists of the volume of the cylinder plus the volume of the aluminum can and the two air hoses. The
millimeter scale
on the cylinder will allow you to directly measure the cylinder's height.
When the piston undergoes transitions in which one or more of the system's properties (P, V, or T) change, the data can be potted on a P-V diagram. Any work done by the system during a transition can be found as the area of the graph bounded by the x-axis (volume axis) and that process' graph. The processes that can be applicable to our heat engine's cycle are limited to isovolumetric, isothermal, isobaric, and adiabatic.
The total work done during a complete cycle is represented by the area of the closed cycle on the P-V diagram.
It is important to take your measurements of temperature, pressure, and piston height as quickly as possible after each transition stabilizes since the apparatus does leak air slightly and you want the completed cycle to return to its initial conditions providing you with a closed PV diagram to analyze.
This is a “real” 4-step heat engine that has expansion and compression processes in which the engine will do useful mechanical work by lifting a 100-gram mass (and the piston) from one height to another. During the expansion steps the gas lifts the mass and piston increasing their potential energy; while during the compression steps their potential energy is reduced. Remember that potential energy is calculated with the equation PE = mgΔy. A diagram of the four steps is shown below:
When your experimental data has been plotted on a P-V diagram, it will hopefully ressemble the diagram below where there is a close agreement between the state variables for Point A (P, V, T) and the values for the cycle's initial preparation conditions.
Notice that steps BC and DA are isobaric processes and steps AB (hopefully the conditions at the engine's preparation and those at the end of the cycle will be synonymous) and CD are isothermal processes.
Air Calculations
You must first calculate the total volume of air in the system that
does not change with the height of the piston
. Remember that this volume includes the volume of the metal canister and the volume of the air in the tubing. The volume of a cylinder equals
.
What is the interior volume of air in the metal canister in m
^{3}
?
What is the interior volume of air in the tubing in m
^{3}
if it has an interior diameter of 0.4 cm?
What is the total volume that air can occupy in the metal canister and tubing during the experiment?
The Experiment
After you have practiced running the cycle several times - the canister transfers, reading the probe values for temperature and pressure, the height at the base of the piston (mm), and carefully adding/removing the 100-gram mass from the top of the piston - you are ready to record the values for a complete cycle. Remember to move as quickly as possible after each step stabilizes.
pressure
temperature
height
of piston
total volume
of air
piston chamber + metal cylinder + tubing
position
(Pa)
(K)
(m)
(m
^{3}
)
preparation
B
C
D
end of cycle
Use the ideal gas law to determine the amount of gas present in the system at each point in the cycle. Use the exact values for the "five" positions since your final step returning to the cold-water bath without the 100-gram mass might not be identical to the preparation conditions.
air present
position
(moles)
preparation
B
C
D
end of cycle
How many moles of air leaked out of the system during the cycle?
If air has a molar mass of 29 g/mole, how many grams of air leaked out of the system during the cycle?
Analysis and Conclusions
Construct a scaled P-V diagram of your entire cycle - plot all "five" data points: preparation, B, C, D, A. Your axes do not need to start at the origin since you will only be examining the interior of the cycle. Next decide whether to use the "preparation" position or the final position as "A." Calculate the area of your cycle. You may assume that the area is a quadrilateral.
Based on your P-V diagram, are you going to use the values for the preparation stage of the experiment or the last values of P, V, and T when the piston returned to the ice-water bath at the end of the cycle as your values for point "A"?
preparation
B
C
D
end of cycle
Explain your choice in the previous answer.
What is the net work done by your heat engine? Give your answer in Joules.
Now you will calculate the effective work done on the piston and 100-gram mass during each process of the cycle. Our expectations are that this effective work will be reasonably close to the area of your P-V diagram previously calculated.
Δ(height)
total mass
ΔPE
process
(m)
(kg)
(J)
AB
BC
CD
DA
What was the total change in potential energy throughout the entire cycle?
What is the percent difference between the net work calculated as the area of your P-V diagram and the net change in PE of the piston and 100-gram mass?
Calculate the heat added using Q
_{in}
= nC
_{P}
ΔT for step BC. Since air is a polyatomic gas, use C
_{P}
= 7/2 nR.
Calculate the actual efficiency of your heat engine by using the change in PE as the effective work done and the heat added found in your previous answer. Express your answer in decimal (not %) form.
Calculate the Carnot efficiency of your heat engine? Express your answer in decimal (not %) form.
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