Adiabatic - Revision history

Dylan.Chung: /* Variation in the Ideal Gas Law */

2026-04-10T16:14:18Z

Variation in the Ideal Gas Law

← Older revision		Revision as of 16:14, 10 April 2026
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	<div displaystyle="text-align:center;">		<div displaystyle="text-align:center;">
	<math>pV^{\gamma}=constant</math>		<math>pV^{\ \gamma}=constant</math>
	</div>		</div>

Dylan.Chung: /* Variation in the Ideal Gas Law */

2026-04-10T16:10:43Z

Variation in the Ideal Gas Law

← Older revision		Revision as of 16:10, 10 April 2026
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	<center><math>pV^{\gamma}=constant</math></~~center~~>		<div displaystyle="text-align:center;">
			<math>pV^{\gamma}=constant</math>
			</div>

	where:		where:
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	*<math>V</math> is volume		*<math>V</math> is volume

	*<math>γ</math> is gamma, which represents the [[specific heat ratio]] defined as:		*<math>\gamma</math> is gamma, which represents the [[specific heat ratio]] defined as:

	::1.67 for a ''monatomic'' gas		::1.67 for a ''monatomic'' gas

Dylan.Chung: /* Variation in the Ideal Gas Law */

2026-04-10T16:09:48Z

Variation in the Ideal Gas Law

← Older revision		Revision as of 16:09, 10 April 2026
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	<center><math>pV^{γ}=constant</math></center>		<center><math>pV^{\gamma}=constant</math></center>

	where:		where:

Jmdonev: 1 revision imported

2021-12-20T19:47:15Z

1 revision imported

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(No difference)

energy>Jmdonev at 19:16, 22 October 2021

2021-10-22T19:16:31Z

← Older revision		Revision as of 19:16, 22 October 2021
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	[[Category:Done ~~2018~~-07-20]]		[[Category:Done 2021-10-29]]
	[[File:Adiabatic_process (1).png\|frame\|400px\|Figure 1: The purple line is an example of an adiabat on a [[PV diagram]]]]		[[File:Adiabatic_process (1).png\|frame\|400px\|Figure 1: The purple line is an example of an adiabat on a [[PV diagram]]]]
	<onlyinclude>'''Adiabatic''' refers to a process in which no [[heat]] is transferred into or out of a [[system]], and the change in [[internal energy]] is only done by [[work]].</onlyinclude> Often ~~this is~~ accomplished in an insulated container, where the process happens too quickly for heat to be transferred. Since heat moves because of a difference in [[temperature]] between a system and its surroundings, an adiabatic process can also happen when the system is in [[thermal equilibrium]].<ref name=gould>H. Gould and J. Tobochnik, "Quasistatic Adiabatic Processes," in ''Statistical and Thermal Physics'', 1st ed., Princeton, NJ: Princeton University Press, 2010, ch.2, sec.11, pp. 51-55</ref> ~~By the~~ [[first law of thermodynamics]], ~~this then looks like~~		<onlyinclude>'''Adiabatic''' refers to a process in which no [[heat]] is transferred into or out of a [[system]], and the change in [[internal energy]] is only done by [[work]]. Most processes in thermodynamics are [[diabatic]] which means they transfer heat. The 'a' at the start of the word adiabatic means without, so 'adiabatic' means 'no heat transfer'.</onlyinclude> Often adiabatic processes are accomplished in an insulated container, where the process happens too quickly for heat to be transferred. Since heat moves because of a difference in [[temperature]] between a system and its surroundings, an adiabatic process can also happen when the system is in [[thermal equilibrium]].<ref name=gould>H. Gould and J. Tobochnik, "Quasistatic Adiabatic Processes," in ''Statistical and Thermal Physics'', 1st ed., Princeton, NJ: Princeton University Press, 2010, ch.2, sec.11, pp. 51-55</ref> The [[first law of thermodynamics]] can be expressed mathematically as:

			<center><math>\Delta U = Q + W = 0</math></center>

			And because the heat (<math>Q</math>) is zero, the expression simplifies to:

	<center><math>\Delta U=W</math></center>		<center><math>\Delta U=W</math></center>
Line 8:		Line 12:

	*<math>\Delta U</math> is the change in the system's internal energy and		*<math>\Delta U</math> is the change in the system's internal energy and
	*<math>W</math> is the work done ''on'' the system (if the system ''does'' work to its surroundings, the work is negative and the systems internal energy ~~thereby~~ decreases).		*<math>W</math> is the work done ''on'' the system (if the system ''does'' work to its surroundings, the work is negative and the systems internal energy and temperature both decreases).

	For an adiabatic ''compression'' (decreasing the [[volume]] of the system, like a [[piston]]), the temperature must increase. Likewise, for an ''expansion'' (increasing volume), the temperature must decrease. This is because there is no heat able to flow in or out in order to balance the temperature, which is what occurs in an [[isothermal]] process.		For an adiabatic ''compression'' (decreasing the [[volume]] of the system, like a [[piston]]), the temperature must increase. Likewise, for an ''expansion'' (increasing volume), the temperature must decrease. This is because there is no heat able to flow in or out in order to balance the temperature, which is what occurs in an [[isothermal]] process.
	~~==Variation in Ideal Gas Law==~~
	[[Isothermal\|Isotherms]] and adiabats may look similar at first glance, but in Figure 1, it's clear that adiabats exhibit much steeper curves. Therefore, the [[ideal gas law]] slightly differs too, as seen in the equation below:

	~~<center><math>pV^{γ}~~=~~constant</math></center>~~ <ref name = knight> [2]R. Knight, Physics for scientists and engineers, 2nd ed. San Francisco: Pearson Addison Wesley, 2008, p. 527. </ref>		==Variation in the Ideal Gas Law==
			[[Isothermal\|Isotherms]] and adiabats may look similar at first glance, but in Figure 1, it's clear that adiabats exhibit much steeper curves. Therefore, the [[ideal gas law]] slightly differs too, as seen in the equation below:
			<ref name = knight> [2]R. Knight, Physics for scientists and engineers, 2nd ed. San Francisco: Pearson Addison Wesley, 2008, p. 527. </ref>


			<center><math>pV^{γ}=constant</math></center>

	where:		where:
Line 28:		Line 35:
	::1.40 for a ''diatomic'' gas		::1.40 for a ''diatomic'' gas

	The gas law above equals a constant, and it does so because the changes in temperature can be encompassed in this formula by measuring the changes in pressure and volume. Mathematically, an integration was done to solve for this formula—and a constant is always added to the equation being integrated—resulting in the constant seen in the equation.		The gas law above equals a constant, and it does so because the changes in temperature can be encompassed in this formula by measuring the changes in pressure and volume. Mathematically, integration was done to solve for this formula—and a constant is always added to the equation being integrated—resulting in the constant seen in the equation.

	To get a detailed derivation of the modified ideal gas law click [http://farside.ph.utexas.edu/teaching/sm1/lectures/node50.html here]		To get a detailed derivation of the modified ideal gas law click [http://farside.ph.utexas.edu/teaching/sm1/lectures/node50.html here].

	==Application==		==Application==
	Adiabatic processes are used in the [[Otto cycle]] (when the piston does work on the gasoline) and [[Brayton cycle]]s within [[gas turbine]]s. [[Diesel engine]]s also make use of a (somewhat) adiabatic compression in order to [[ignition\|ignite]] its [[fuel]]. Adiabats are also important for the derivation of the [[Carnot efficiency]] (the maximum [[thermal efficiency]] of any thermodynamic system) which relies on two adiabatic processes.<ref name=Knight>R. D. Knight, "The Limits of Efficiency" in ''Physics for Scientists and Engineers: A Strategic Approach,'' 3nd ed. San Francisco, U.S.A.: Pearson Addison-Wesley, 2008, ch.19, sec.5, pp. 540-542</ref>		Adiabatic processes are used in the [[Otto cycle]] (when the piston does work on the gasoline) and [[Brayton cycle]]s within [[gas turbine]]s. [[Diesel engine]]s also make use of a (somewhat) adiabatic compression in order to [[ignition\|ignite]] its [[fuel]]. Adiabats are also important for the derivation of the [[Carnot efficiency]] (the maximum [[thermal efficiency]] of any thermodynamic system) which relies on two adiabatic processes.<ref name=Knight>R. D. Knight, "The Limits of Efficiency" in ''Physics for Scientists and Engineers: A Strategic Approach,'' 3nd ed. San Francisco, U.S.A.: Pearson Addison-Wesley, 2008, ch.19, sec.5, pp. 540-542</ref>

	The video below (from [http://www.teachersource.com/ Educational Innovations, Inc.]) demonstrates an adiabatic compression: the temperature inside the chamber is increased enough to ignite cotton.		The video below (from [http://www.teachersource.com/ Educational Innovations, Inc.]) demonstrates an adiabatic compression: the temperature inside the chamber is increased enough to ignite the cotton.

	<html>		<html>
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	==For Further Reading==		==For Further Reading==
	~~Changing the design of a house can drastically alter its energy efficiency. See [[energy efficient building design]] to~~ learn more or explore one of the pages below:		To learn more or explore one of the pages below:
	*[[Isothermal]]		*[[Isothermal]]
	*[[Isobar (pressure)]]		*[[Isobar (pressure)]]
	*[[Isochore]]		*[[Isochore (volume)]]
	*[[Ideal gas law]]		*[[Ideal gas law]]
	*[[First law of thermodynamics]]		*[[First law of thermodynamics]]

Jmdonev: 1 revision imported

2018-07-21T01:12:56Z

1 revision imported

← Older revision	Revision as of 01:12, 21 July 2018
(No difference)

Jmdonev at 19:10, 27 June 2018

2018-06-27T19:10:31Z

← Older revision		Revision as of 19:10, 27 June 2018
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	[[Category:Done 2018-06-15]]		[[Category:Done 2018-07-20]]
	[[File:Adiabatic_process (1).png\|frame\|400px\|Figure 1: The purple line is an example of an adiabat on a [[PV diagram]]]]		[[File:Adiabatic_process (1).png\|frame\|400px\|Figure 1: The purple line is an example of an adiabat on a [[PV diagram]]]]
	<onlyinclude>'''Adiabatic''' refers to a process in which no [[heat]] is transferred into or out of a [[system]], and the change in [[internal energy]] is only done by [[work]].</onlyinclude> Often this is accomplished in an insulated container, where the process happens too quickly for heat to be transferred. Since heat moves because of a difference in [[temperature]] between a system and its surroundings, an adiabatic process can also happen when the system is in [[thermal equilibrium]].<ref name=gould>H. Gould and J. Tobochnik, "Quasistatic Adiabatic Processes," in ''Statistical and Thermal Physics'', 1st ed., Princeton, NJ: Princeton University Press, 2010, ch.2, sec.11, pp. 51-55</ref> By the [[first law of thermodynamics]], this then looks like		<onlyinclude>'''Adiabatic''' refers to a process in which no [[heat]] is transferred into or out of a [[system]], and the change in [[internal energy]] is only done by [[work]].</onlyinclude> Often this is accomplished in an insulated container, where the process happens too quickly for heat to be transferred. Since heat moves because of a difference in [[temperature]] between a system and its surroundings, an adiabatic process can also happen when the system is in [[thermal equilibrium]].<ref name=gould>H. Gould and J. Tobochnik, "Quasistatic Adiabatic Processes," in ''Statistical and Thermal Physics'', 1st ed., Princeton, NJ: Princeton University Press, 2010, ch.2, sec.11, pp. 51-55</ref> By the [[first law of thermodynamics]], this then looks like
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	==For Further Reading==		==For Further Reading==
	Changing the design of a house can ~~drasitally~~ alter its energy efficiency. See [[energy efficient building design]] to learn more or explore one of the pages below:		Changing the design of a house can drastically alter its energy efficiency. See [[energy efficient building design]] to learn more or explore one of the pages below:
	*[[Isothermal]]		*[[Isothermal]]
	*[[Isobar (pressure)]]		*[[Isobar (pressure)]]
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	==References==		==References==
	{{reflist}}		{{reflist}}
			[[Category:Uploaded]]

Jmdonev: 1 revision imported

2018-06-25T14:30:27Z

1 revision imported

← Older revision	Revision as of 14:30, 25 June 2018
(No difference)

Jmdonev at 00:27, 9 June 2018

2018-06-09T00:27:28Z

← Older revision		Revision as of 00:27, 9 June 2018
Line 1:		Line 1:
	[[Category:Done ~~2015~~-09-06]]		[[Category:Done 2018-06-15]]
			[[File:Adiabatic_process (1).png\|frame\|400px\|Figure 1: The purple line is an example of an adiabat on a [[PV diagram]]]]
	<onlyinclude>'''Adiabatic''' refers to a process in which no [[heat]] is transferred into or out of a [[system]], and the change in [[internal energy]] is only done by [[work]].</onlyinclude> Often this is accomplished in an insulated container, where the process happens too quickly for heat to be transferred. Since heat moves because of a difference in [[temperature]] between a system and its surroundings, an adiabatic process can also happen when the system is in [[thermal equilibrium]].<ref name=gould>H. Gould and J. Tobochnik, "Quasistatic Adiabatic Processes," in ''Statistical and Thermal Physics'', 1st ed., Princeton, NJ: Princeton University Press, 2010, ch.2, sec.11, pp. 51-55</ref> By the [[first law of thermodynamics]], this then looks like		<onlyinclude>'''Adiabatic''' refers to a process in which no [[heat]] is transferred into or out of a [[system]], and the change in [[internal energy]] is only done by [[work]].</onlyinclude> Often this is accomplished in an insulated container, where the process happens too quickly for heat to be transferred. Since heat moves because of a difference in [[temperature]] between a system and its surroundings, an adiabatic process can also happen when the system is in [[thermal equilibrium]].<ref name=gould>H. Gould and J. Tobochnik, "Quasistatic Adiabatic Processes," in ''Statistical and Thermal Physics'', 1st ed., Princeton, NJ: Princeton University Press, 2010, ch.2, sec.11, pp. 51-55</ref> By the [[first law of thermodynamics]], this then looks like

	<center><m>\Delta U=W</m></center>		<center><math>\Delta U=W</math></center>

	where:		where:

	*<m>\Delta U</m> is the change in the system's internal energy and		*<math>\Delta U</math> is the change in the system's internal energy and
	*<m>W</m> is the work done ''on'' the system (if the system ''does'' work to its surroundings, the work is negative and the systems internal energy thereby decreases).		*<math>W</math> is the work done ''on'' the system (if the system ''does'' work to its surroundings, the work is negative and the systems internal energy thereby decreases).

	For an adiabatic ''compression'' (decreasing the [[volume]] of the system, like a [[piston]]), the temperature must increase. Likewise, for an ''expansion'' (increasing volume), the temperature must decrease. This is because there is no heat able to flow in or out in order to balance the temperature, which is what occurs in an [[isothermal]] process.		For an adiabatic ''compression'' (decreasing the [[volume]] of the system, like a [[piston]]), the temperature must increase. Likewise, for an ''expansion'' (increasing volume), the temperature must decrease. This is because there is no heat able to flow in or out in order to balance the temperature, which is what occurs in an [[isothermal]] process.
			==Variation in Ideal Gas Law==
			[[Isothermal\|Isotherms]] and adiabats may look similar at first glance, but in Figure 1, it's clear that adiabats exhibit much steeper curves. Therefore, the [[ideal gas law]] slightly differs too, as seen in the equation below:

	Adiabatic processes are used in the [[Brayton cycle]] within [[gas turbine]]s. [[Diesel engine]]s also make use of a (somewhat) adiabatic compression in order to [[ignition\|ignite]] its [[fuel]]. Adiabats are also important for the derivation of the [[Carnot efficiency]] (the maximum [[thermal efficiency]] of any thermodynamic system) which relies on two adiabatic processes.<ref name=Knight>R. D. Knight, "The Limits of Efficiency" in ''Physics for Scientists and Engineers: A Strategic Approach,'' 3nd ed. San Francisco, U.S.A.: Pearson Addison-Wesley, 2008, ch.19, sec.5, pp. 540-542</ref>		<center><math>pV^{γ}=constant</math></center> <ref name = knight> [2]R. Knight, Physics for scientists and engineers, 2nd ed. San Francisco: Pearson Addison Wesley, 2008, p. 527. </ref>

			where:

			*<math>p</math> is pressure

			*<math>V</math> is volume

			*<math>γ</math> is gamma, which represents the [[specific heat ratio]] defined as:

			::1.67 for a ''monatomic'' gas

			::1.40 for a ''diatomic'' gas

			The gas law above equals a constant, and it does so because the changes in temperature can be encompassed in this formula by measuring the changes in pressure and volume. Mathematically, an integration was done to solve for this formula—and a constant is always added to the equation being integrated—resulting in the constant seen in the equation.

			To get a detailed derivation of the modified ideal gas law click [http://farside.ph.utexas.edu/teaching/sm1/lectures/node50.html here]

			==Application==
			Adiabatic processes are used in the [[Otto cycle]] (when the piston does work on the gasoline) and [[Brayton cycle]]s within [[gas turbine]]s. [[Diesel engine]]s also make use of a (somewhat) adiabatic compression in order to [[ignition\|ignite]] its [[fuel]]. Adiabats are also important for the derivation of the [[Carnot efficiency]] (the maximum [[thermal efficiency]] of any thermodynamic system) which relies on two adiabatic processes.<ref name=Knight>R. D. Knight, "The Limits of Efficiency" in ''Physics for Scientists and Engineers: A Strategic Approach,'' 3nd ed. San Francisco, U.S.A.: Pearson Addison-Wesley, 2008, ch.19, sec.5, pp. 540-542</ref>

	The video below (from [http://www.teachersource.com/ Educational Innovations, Inc.]) demonstrates an adiabatic compression: the temperature inside the chamber is increased enough to ignite cotton.		The video below (from [http://www.teachersource.com/ Educational Innovations, Inc.]) demonstrates an adiabatic compression: the temperature inside the chamber is increased enough to ignite cotton.
Line 19:		Line 41:

	<center>See [http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html Hyperphysics] for more information.</center>		<center>See [http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html Hyperphysics] for more information.</center>

			==For Further Reading==
			Changing the design of a house can drasitally alter its energy efficiency. See [[energy efficient building design]] to learn more or explore one of the pages below:
			*[[Isothermal]]
			*[[Isobar (pressure)]]
			*[[Isochore]]
			*[[Ideal gas law]]
			*[[First law of thermodynamics]]
			*Or explore a [[Special:Random\| random page]]

	==References==		==References==
	{{reflist}}		{{reflist}}

J.williams: 1 revision imported

2015-09-18T16:52:27Z

1 revision imported

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