Heat - Revision history

Lwcamp at 19:01, 7 March 2026

2026-03-07T19:01:04Z

← Older revision		Revision as of 12:01, 7 March 2026
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	Authors: Luke Campbell, Rocketman1999, and Tshhmon		Authors: Luke Campbell, Rocketman1999, and Tshhmon

	[[Category:Physics & Engineering]]		[[Category:Physics & Engineering]][[Category:Physics & Math & Engineering]]

Lwcamp: /* Heat Management */

2026-02-24T16:16:46Z

Heat Management

← Older revision		Revision as of 09:16, 24 February 2026
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	==Heat Management==		==Heat Management==
	~~'''~~[[Heat Management]]~~'''~~
			When you do stuff, you always end up making some entropy. In order to get rid of this entropy, you need to move it somewhere outside of your system as heat. [[Heat Management\|Heat management]] is about how to do this.

	=Additional reading=		=Additional reading=

Lwcamp: /* Heat engines */

2026-02-24T16:15:15Z

Heat engines

← Older revision		Revision as of 09:15, 24 February 2026
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	=Heat engines=		=Heat engines=
	~~'''~~[[Heat Engines]]~~'''~~
			A heat engine is any device that takes in energy and entropy from a high temperature heat source and then gets rid of the entropy (and some of the energy) by dumping it into a lower temperature heat sink. The remaining energy can be used to do work. This can include devices such as steam engines, internal combustion piston engines, gas turbines, steam turbines, and even solar panels (which take in energy and entropy from the nearly 6000 K sun and exhaust the excess entropy and the energy needed to go with it into the approximately 300 K environment). The main page on heat engines is [[Heat Engines\|here]].

	=Onwards to practice=		=Onwards to practice=

Lwcamp: /* Enthalpy */

2026-02-18T03:22:29Z

Enthalpy

← Older revision		Revision as of 20:22, 17 February 2026
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	=Thermal properties=		=Thermal properties=
	==Enthalpy==		==Enthalpy==
	~~Enthalpy is~~ the ~~sum~~ of a system'~~s internal energy and~~ the ~~product~~ of ~~its~~ pressure ~~and volume~~. When we consider phases of matter (solid, gas, liquid, et cetera) as thermodynamic systems we find that transitioning from a phase to another requires adding or removing energy from that material. This is ~~also~~ referred to as the enthalpy of a particular phase transition (e.g. enthalpy of vaporization; or, boiling.)
			Often, you want to work on a system at constant pressure from the surrounding environment. If the system expands by a volume Δ<i>V</i> as you do stuff to it, the system will do work of <i>p</i> Δ<i>V</i> on the environment. This work done on the environment is lost from your system and you can't use it for other things. If the system contracts by -Δ<i>V</i>, then the environment does work of <i>p</i> Δ<i>V</i> on the system; this is work you get for free. The effective work done on the system is the actual work plus <i>p</i> Δ<i>V</i>.

			Therefore, for systems operating at constant pressure (like a chemical reaction or phase transition occurring in open air exposed to the environment), it is useful to define the <i>Enthalpy</i> as
			<div align=center>
			<i>H</i> = <i>U</i> + <i>p</i> Δ<i>V</i>
			</div>
			to account for this free energy, where <i>U</i> is the energy internal to the system.

			When we consider phases of matter (solid, gas, liquid, et cetera) as thermodynamic systems we find that transitioning from a phase to another requires adding or removing energy from that material. Because this usually happens at constant pressure, it is useful to charactarize this by the enthalpy of the system; where the amount of energy that you have to give the system is the difference in enthalpy between the two states. This is referred to as the enthalpy of a particular phase transition (e.g. enthalpy of vaporization; or, boiling.)

	When we consider the process in reverse (e.g. the enthalpy of condensation), the enthalpy is also equal and opposite. These enthalpies also change with ambient conditions such as temperature and pressure; we often measure enthalpies at what's called "standard temperature and pressure (STP)". Of course, there are differing standards. In the United States, one common standard comes from the National Institute of Standards and Technology (NIST). This standard specifies STP to be 293.15 degrees Kelvin and 1 (Earth) atmosphere of pressure (101,325 Pa). Some common other terminologies for enthalpy are: heat of..., or latent heat of....		When we consider the process in reverse (e.g. the enthalpy of condensation), the enthalpy is also equal and opposite. These enthalpies also change with ambient conditions such as temperature and pressure; we often measure enthalpies at what's called "standard temperature and pressure (STP)". Of course, there are differing standards. In the United States, one common standard comes from the National Institute of Standards and Technology (NIST). This standard specifies STP to be 293.15 degrees Kelvin and 1 (Earth) atmosphere of pressure (101,325 Pa). Some common other terminologies for enthalpy are: heat of..., or latent heat of....

	Enthalpy can be measured according to volume or mass or amount of substance~~; the SI units for measuring enthalpy are:~~ joules per cubic meter (J/m<sup>3</sup>); gram (J/g); or, mole (J/mol).		Enthalpy has units of energy, in the SI system this is joules (J). It can be measured according to volume or mass or amount of substance, you commonly see enthalpies listed as joules per cubic meter (J/m<sup>3</sup>), joules per gram (J/g), or joules per mole (J/mol).

	==Heat capacity==		==Heat capacity==

Lwcamp: /* Enthalpy */

2026-02-18T02:44:14Z

Enthalpy

← Older revision		Revision as of 19:44, 17 February 2026
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	Enthalpy is the sum of a system's internal energy and the product of its pressure and volume. When we consider phases of matter (solid, gas, liquid, et cetera) as thermodynamic systems we find that transitioning from a phase to another requires adding or removing energy from that material. This is also referred to as the enthalpy of a particular phase transition (e.g. enthalpy of vaporization; or, boiling.)		Enthalpy is the sum of a system's internal energy and the product of its pressure and volume. When we consider phases of matter (solid, gas, liquid, et cetera) as thermodynamic systems we find that transitioning from a phase to another requires adding or removing energy from that material. This is also referred to as the enthalpy of a particular phase transition (e.g. enthalpy of vaporization; or, boiling.)

	When we consider the process in reverse (e.g. the enthalpy of condensation), the enthalpy is also equal and opposite. These enthalpies also change with ambient conditions such as temperature and pressure; we often measure enthalpies at what's called "standard temperature and pressure (STP)". Of course, there are differing standards. In the United States, one common standard comes from the National Institute of Standards and Technology (NIST). This standard specifies STP to be 293.15 degrees Kelvin and 1 (Earth) atmosphere of pressure. Some common other terminologies for enthalpy are: heat of..., or latent heat of....		When we consider the process in reverse (e.g. the enthalpy of condensation), the enthalpy is also equal and opposite. These enthalpies also change with ambient conditions such as temperature and pressure; we often measure enthalpies at what's called "standard temperature and pressure (STP)". Of course, there are differing standards. In the United States, one common standard comes from the National Institute of Standards and Technology (NIST). This standard specifies STP to be 293.15 degrees Kelvin and 1 (Earth) atmosphere of pressure (101,325 Pa). Some common other terminologies for enthalpy are: heat of..., or latent heat of....

	Enthalpy can be measured according to volume or mass or amount of substance; the SI units for measuring enthalpy are: joules per cubic meter (J/m<sup>3</sup>); gram (J/g); or, mole (J/mol).		Enthalpy can be measured according to volume or mass or amount of substance; the SI units for measuring enthalpy are: joules per cubic meter (J/m<sup>3</sup>); gram (J/g); or, mole (J/mol).

	==Heat capacity==		==Heat capacity==

Lwcamp: /* Radiation */

2026-02-18T02:42:16Z

Radiation

← Older revision		Revision as of 19:42, 17 February 2026
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	</div>		</div>
	and individually they are all between 0 and 1. The quantity <i>a(ω)</i> is called the absorptivity, <i>r(ω)</i> the reflectivity, and <i>t(ω)</i> the transmissivity.		and individually they are all between 0 and 1. The quantity <i>a(ω)</i> is called the absorptivity, <i>r(ω)</i> the reflectivity, and <i>t(ω)</i> the transmissivity.
	For a black body, <i>a(ω)</i> = 1 for all ω. If this is not the case, the power radiated away at that frequency is decreased by a factor of <i>a(ω)</i>. If the absorptivity is roughly the same over the spectral range where the object is radiating, its radiated power is overall decreased by a factor of <i>a(ω)</i>. Absorptivity decreases both the absorption and emission at a given wavelength equally; the amount of decrease from a black body is often called <i>emissivity</i> (ε(ω)). Because ε(ω) = <i>a(ω)</i>, emissivity and absorptivity ~~are often~~ used interchangeably.		For a black body, <i>a(ω)</i> = 1 for all ω. If this is not the case, the power radiated away at that frequency is decreased by a factor of <i>a(ω)</i>. If the absorptivity is roughly the same over the spectral range where the object is radiating, its radiated power is overall decreased by a factor of <i>a(ω)</i>. Absorptivity decreases both the absorption and emission at a given wavelength equally; the amount of decrease from a black body is often called <i>emissivity</i> (ε(ω)). Because ε(ω) = <i>a(ω)</i>, emissivity and absorptivity can be used interchangeably.

	=Thermal properties=		=Thermal properties=

Lwcamp: /* Radiation */

2026-02-18T02:41:34Z

Radiation

← Older revision		Revision as of 19:41, 17 February 2026
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	</div>		</div>
	and individually they are all between 0 and 1. The quantity <i>a(ω)</i> is called the absorptivity, <i>r(ω)</i> the reflectivity, and <i>t(ω)</i> the transmissivity.		and individually they are all between 0 and 1. The quantity <i>a(ω)</i> is called the absorptivity, <i>r(ω)</i> the reflectivity, and <i>t(ω)</i> the transmissivity.
	For a black body, <i>a(ω)</i> = 1 for all ω. If this is not the case, the power radiated away at that frequency is decreased by a factor of <i>a(ω)</i>. If the absorptivity is roughly the same over the spectral range where the object is radiating, its radiated power is overall decreased by a factor of <i>a(ω)</i>.		For a black body, <i>a(ω)</i> = 1 for all ω. If this is not the case, the power radiated away at that frequency is decreased by a factor of <i>a(ω)</i>. If the absorptivity is roughly the same over the spectral range where the object is radiating, its radiated power is overall decreased by a factor of <i>a(ω)</i>. Absorptivity decreases both the absorption and emission at a given wavelength equally; the amount of decrease from a black body is often called <i>emissivity</i> (ε(ω)). Because ε(ω) = <i>a(ω)</i>, emissivity and absorptivity are often used interchangeably.

	=Thermal properties=		=Thermal properties=

Lwcamp: /* Radiation */

2026-02-18T02:38:12Z

Radiation

← Older revision		Revision as of 19:38, 17 February 2026
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	where σ<sub>SB</sub> = 5.670373 × 10<sup>-8</sup> W/m<sup>2</sup>/K<sup>4</sup> is the Stefan–Boltzmann constant. That fourth power of temperature in there means that the power radiated per unit area goes up <i>very</i> quickly with increasing temperature – doubling the temperature gives sixteen times as much radiation!		where σ<sub>SB</sub> = 5.670373 × 10<sup>-8</sup> W/m<sup>2</sup>/K<sup>4</sup> is the Stefan–Boltzmann constant. That fourth power of temperature in there means that the power radiated per unit area goes up <i>very</i> quickly with increasing temperature – doubling the temperature gives sixteen times as much radiation!

	Objects that are not black will radiate at a reduced power level. In general at a specific frequency of electromagnetic radiation ~~<math>\~~omega~~</math>~~, an object will reflect away a fraction <~~math~~>r(\omega)</~~math~~>, transmit through a fraction <~~math~~>t(\omega)</~~math~~>, and absorb a fraction <~~math~~>a(\omega)</~~math~~>. Together, these must all add up to one		Objects that are not black will radiate at a reduced power level. In general at a specific frequency of electromagnetic radiation ω, an object will reflect away a fraction <i>r(ω)</i>, transmit through a fraction <i>t(ω)</i>, and absorb a fraction <i>a(ω)</i>. Together, these must all add up to one
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><~~math~~>		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
	r(\omega) + t(\omega) + a(\omega) = 1		<i>r(ω)</i> + <i>t(ω)</i> + <i>a(ω)</i> = 1
	~~</math>~~</div>		</div>
	and individually they are all between 0 and 1. The quantity <~~math~~>a(\omega)</~~math~~> is called the absorptivity, <~~math~~>r(\omega)</~~math~~> the reflectivity, and <~~math~~>t(\omega)</~~math~~> the transmissivity.		and individually they are all between 0 and 1. The quantity <i>a(ω)</i> is called the absorptivity, <i>r(ω)</i> the reflectivity, and <i>t(ω)</i> the transmissivity.
	For a black body, <~~math~~>a(\omega)=1</~~math~~> for all ~~<math>\~~omega~~</math>~~. If this is not the case, the power radiated away at that frequency is decreased by a factor of <~~math~~>a(\omega)</~~math~~>. If the absorptivity is roughly the same over the spectral range where the object is radiating, its radiated power is overall decreased by a factor of <~~math~~>a</~~math~~>.		For a black body, <i>a(ω)</i> = 1 for all ω. If this is not the case, the power radiated away at that frequency is decreased by a factor of <i>a(ω)</i>. If the absorptivity is roughly the same over the spectral range where the object is radiating, its radiated power is overall decreased by a factor of <i>a(ω)</i>.

	=Thermal properties=		=Thermal properties=

Lwcamp: /* Radiation */

2026-02-18T02:34:31Z

Radiation

← Older revision		Revision as of 19:34, 17 February 2026
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	<i>I</i> = σ<sub>SB</sub> <i>T </i><sup>4</sup>		<i>I</i> = σ<sub>SB</sub> <i>T </i><sup>4</sup>
	</div>		</div>
	where <~~math~~>~~\sigma_{~~SB} = 5.670373 \times 10^{-8}</~~math~~> W/m~~²~~/K^4 is the Stefan–Boltzmann constant. That fourth power of temperature in there means that the power radiated per unit area goes up <i>very</i> quickly with increasing temperature – doubling the temperature gives sixteen times as much radiation!		where σ<sub>SB</sub> = 5.670373 × 10<sup>-8</sup> W/m<sup>2</sup>/K<sup>4</sup> is the Stefan–Boltzmann constant. That fourth power of temperature in there means that the power radiated per unit area goes up <i>very</i> quickly with increasing temperature – doubling the temperature gives sixteen times as much radiation!

	Objects that are not black will radiate at a reduced power level. In general at a specific frequency of electromagnetic radiation <math>\omega</math>, an object will reflect away a fraction <math>r(\omega)</math>, transmit through a fraction <math>t(\omega)</math>, and absorb a fraction <math>a(\omega)</math>. Together, these must all add up to one		Objects that are not black will radiate at a reduced power level. In general at a specific frequency of electromagnetic radiation <math>\omega</math>, an object will reflect away a fraction <math>r(\omega)</math>, transmit through a fraction <math>t(\omega)</math>, and absorb a fraction <math>a(\omega)</math>. Together, these must all add up to one

Lwcamp: /* Radiation */

2026-02-18T02:33:12Z

Radiation

← Older revision		Revision as of 19:33, 17 February 2026
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	When a system is in thermal equilibrium with the electromagnetic field, it is said to behave as a black body. It gets this name because an object that absorbs all light that hits it will be in equilibrium with the electromagnetic field. A black body radiates across a wide range of frequencies, but the peak frequency will be at		When a system is in thermal equilibrium with the electromagnetic field, it is said to behave as a black body. It gets this name because an object that absorbs all light that hits it will be in equilibrium with the electromagnetic field. A black body radiates across a wide range of frequencies, but the peak frequency will be at
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><~~math~~>		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
	~~\lambda_{\rm~~ peak} = 2898 ~~\, \~~mu~~{\rm~~ m} / T(~~{\rm~~ K}).		λ<sub>peak</sub> = 2898 μm / <i>T</i>(K)
	~~</math>~~</div>		</div>
	So as temperature goes up the radiation is primarily emitted at shorter and shorter wavelengths – infrared at room temperature, but shifting ro dull red as temperature increases, then orange, yellow, white, and blue-white.		So as temperature goes up the radiation is primarily emitted at shorter and shorter wavelengths – infrared at room temperature, but shifting to dull red as temperature increases, then orange, yellow, white, and blue-white.

	A black body at a temperature <~~math~~>T</~~math~~> will radiate at an intensity of		A black body at a temperature <i>T</i> will radiate at an intensity of
	<div class="center" style="width: auto; margin-left: auto; margin-right: auto;"><~~math~~>		<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
	I = ~~\sigma_{~~SB~~} \,~~ T^4		<i>I</i> = σ<sub>SB</sub> <i>T </i><sup>4</sup>
	</~~math~~></div>		</div>
	where <math>\sigma_{SB} = 5.670373 \times 10^{-8}</math> W/m²/K^4 is the Stefan–Boltzmann constant. That fourth power of temperature in there means that the power radiated per unit area goes up <i>very</i> quickly with increasing temperature – doubling the temperature gives sixteen times as much radiation!		where <math>\sigma_{SB} = 5.670373 \times 10^{-8}</math> W/m²/K^4 is the Stefan–Boltzmann constant. That fourth power of temperature in there means that the power radiated per unit area goes up <i>very</i> quickly with increasing temperature – doubling the temperature gives sixteen times as much radiation!