Charles' law and gas in a piston
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Charles' law and gas in a piston
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[post_content] => Practice Passage (Question 1-5)
*This passage is the property of Khan Academy and has been reformatted into an AAMC-style interface in their entirety by MedLife Mastery. MedLife Mastery does not endorse and is not an affiliate of Khan Academy.
According to the experiments of Jacques Charles, when a gas within a closed system is heated, the volume increases proportionally, so long as the pressure and moles for the system remain constant. Charles’s law is represented by the following equation:
*Volume can be expressed in metric units. Temperature must be expressed in kelvins.
The flight of a hot air balloon is attributable to Charles’s law. As the air in the balloon is heated, the volume of the air is increased. In this instance, a given weight of hot air occupies a greater volume than the same given weight of cold air, or said differently, the hot air inside the balloon becomes less dense than the surrounding cooler air. The hot air of the balloon (now less dense) begins to rise, culminating in flight. As the air in the balloon is allowed to cool, the density increases, and the basket returns to the ground.
This law can be demonstrated experimentally by observing the change in volume within a piston. The piston is exposed to heat through an incorporated heating coil, which relies on voltage adjustment to control temperature. Heat is released as a result of increased voltage and subsequent increased current passing through the coil. The following table provides the collected data from one such experience, in which volume change is measured by the height of the internal chamber of the piston. Isobaric conditions apply.
Table 1. A list of corresponding heights and volumes at each temperature.
The experimental data adheres closely to ideal gas behavior, and deviations from ideal behavior are negligible.
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[question] => If the piston became locked in place such that chamber volume remained constant, as voltage in the coil increases, how would the internal pressure be affected?
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[answer] => 1
[description] => Reason for the Correct Answer:
Apply the ideal gas law, PV=nRT under constant volume conditions
In a closed container, the number of particles (moles) would also be constant, because gas isn’t being added or removed.
As the voltage increases, more current can flow through the wire, resulting in increased heat production and increased temperature
Pressure would increase, because particle collisions with the container walls are occurring more frequently. This increased frequency of collisions is attributed to the increased gas temperature, and fixed volume and number of moles.
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[each_answer] => A. Pressure would increase, because particle collisions with the container walls are occurring more frequently.
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[1] => Array
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[each_answer] => B. Pressure would increase, because particle collisions with the container walls are occurring less frequently.
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[2] => Array
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[each_answer] => C. Pressure would decrease, because particle collisions with the container walls are occurring more frequently.
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[each_answer] => D. Pressure would decrease, because particle collisions with the container walls are occurring less frequently.
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[1] => Array
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[quiz_unique_key] => 3873426850
[question] => What does Charles’ law state?
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[answer] => 1
[description] => Reason for the Correct Answer:
Charles’s states that under isobaric conditions with constant moles, the temperature and volume of an ideal gas are directly related.
Pressure is not a variable in Charles’s law and must be assumed to be constant when comparing volume and temperature.
According to Charles’s law, at constant pressure, as the temperature of a gas increases, so does the volume.
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[answers] => Array
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[0] => Array
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[each_answer] => A. At constant pressure, as the temperature of a gas increases, so does the volume.
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[1] => Array
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[each_answer] => B. At constant volume, as the gas pressure increases, so does the temperature.
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[2] => Array
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[each_answer] => C. At constant volume, as the gas pressure increases, the temperature decreases.
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[each_answer] => D. At constant temperature, as gas pressure increases, so does the volume.
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[2] => Array
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[quiz_unique_key] => 83407773
[question] => How can an experimentally observed volume of <20π cm3 at -15°C be explained?
[value] => Array
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[answer] => 4
[description] => Reason for the Correct Answer:
This volume is lower than would be predicted by ideal gas laws.
When a gas condenses to a liquid, its volume decreases dramatically.
The gas condenses to liquid at a temperature slightly greater than 15°C. This abnormally small volume could be the result of a phase change. At 15°C, the compound is liquid; therefore, the boiling point is greater than 15°C. At 40°C the compound is a gas, meaning the boiling point is slightly greater than 15°C.
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[answers] => Array
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[0] => Array
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[each_answer] => A. Gases only behave ideally between 0°C and 100°C
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[1] => Array
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[each_answer] => B. At low temperatures, gas particles can effuse from the closed container.
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[each_answer] => C. The gas condenses to a liquid at a temperature slightly below -15°C
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[each_answer] => D. The gas condenses to liquid at a temperature slightly greater than -15°C
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[quiz_unique_key] => 2261298308
[question] => What is the volume of the unknown gas at 140°C?
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[answer] => 2
[description] => Reason for the Correct Answer:
140°C = (273 + 140)K = 413K
Apply the initial conditions from the table (40°C and 160.6π cm3) to the formula: Vɪɴɪᴛɪᴀʟ/ Vɪɴɪᴛɪᴀʟ = Vꜰɪɴᴀʟ/Tꜰɪɴᴀʟ
Vɪɴɪᴛɪᴀʟ / Vɪɴɪᴛɪᴀʟ = Vꜰɪɴᴀʟ/Tꜰɪɴᴀʟ , so (313K/160.6π cm3) = (413K/Vꜰɪɴᴀʟ), and Vꜰɪɴᴀʟ = 211.9π cm3
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[answers] => Array
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[each_answer] => A. 209.2π cm³
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[each_answer] => B. 211.9π cm³
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[each_answer] => C. 213.7π cm³
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[each_answer] => D. 215.6π cm³
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[quiz_unique_key] => 574431310
[question] => How does the experimentally derived volume for a real gas compare to that of a true ideal gas?
[value] => Array
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[answer] => 1
[description] => Reason for the Correct Answer:
Real gases, as opposed to ideal gases, exhibit properties that can’t be explained by the ideal gas law. One property lending to this deviation is real space occupied by particles.
Ideal volume is an exaggeration of actual volume.
ideal volume is greater than observed volume, because real gas particles occupy space. If real gas particles occupy space, then ideal volume is an over approximation of the real (observed) volume.
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[0] => Array
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[each_answer] => A. deal volume is greater than observed volume, because real gas particles occupy space.
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[each_answer] => B. Ideal volume is greater than observed volume, because real gas particles occupy no space.
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[each_answer] => C. Ideal volume is less than observed volume, because real gas particles occupy no space.
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[each_answer] => D. Ideal volume is less than observed volume, because real gas particles occupy space.
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