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The Gibbs–Helmholtz equation is a thermodynamic equation useful for calculating changes in the Gibbs energy of a system as a function of temperature. It is named after Josiah Willard Gibbs and Hermann von Helmholtz.

Equation

The equation is:^[1]

The Aharonov–Casher effect is a quantum mechanical phenomenon in which a traveling magnetic dipole is affected by an electric field. It is dual to the Aharonov–Bohm effect, in which the quantum phase of a charged particle depends upon which side of a magnetic flux tube it comes through. In the Aharonov–Casher effect, the particle has a magnetic moment and the tubes are charged instead. It is used for example to observe interference of neutrons or fluxons.

In both effects the particle acquires some phase shift ( $\varphi$ ) while traveling along some path P. In the Aharonov–Bohm effect it is

\varphi _{AB}={\frac {q}{\hbar }}\int _{P}\mathbf {A} \cdot d\mathbf {x}

While for the Aharonov–Casher effect it is

\varphi _{AC}={\frac {1}{\hbar c^{2}}}\int _{P}(\mathbf {E} \times {\boldsymbol {\mu }})\cdot d\mathbf {x}

where $q$ is its charge and ${\boldsymbol {\mu }}$ is the magnetic moment.

Bibliography

One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
Template:Cite paper

Chemical reactions

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The typical applications are to chemical reactions. The equation reads:^[2]

\left({\frac {\partial (\Delta G^{\ominus }/T)}{\partial T}}\right)_{p}=-{\frac {\Delta H}{T^{2}}}

with ΔG as the change in Gibbs energy and ΔH as the enthalpy change (considered independent of temperature). The o denotes Standard conditions for temperature and pressure (approximately temperature 298.15 Kelvin and pressure 101,325 pascals).

Integrating with respect to T (again p is constant) it becomes:

{\frac {\Delta G^{\ominus }(T_{2})}{T_{2}}}-{\frac {\Delta G^{\ominus }(T_{1})}{T_{1}}}=\Delta H^{\ominus }(p)\left({\frac {1}{T_{2}}}-{\frac {1}{T_{1}}}\right)

This equation quickly enables the calculation of the Gibbs free energy change for a chemical reaction at any temperature T₂ with knowledge of just the Standard Gibbs free energy change of formation and the Standard enthalpy change of formation for the individual components.

Also, using the reaction isotherm equation,^[3] that is

{\frac {\Delta G^{\ominus }}{T}}=-R\ln K

which relates the Gibbs energy to a chemical equilibrium constant, the van 't Hoff equation can be derived.^[4]

Derivation

Background

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.

The definition of the Gibbs function is

H=G+ST\,\!

where H is the enthalpy defined by:

H=U+pV\,\!

Taking differentials of each definition to find dH and dG, then using the fundamental thermodynamic relation, aka "master equation" (always true for reversible or irreversible processes):

dU=TdS-pdV\,\!

where S is the entropy, V is volume, (minus sign due to reversibility, in which dU = 0: work other than pressure-volume may be done and is equal to −pV) leads to the "reversed" form of the initial fundamental relation into a new master equation:

dG=-SdT+Vdp\,\!

This is the Gibbs free energy for a closed system. The Gibbs–Helmholtz equation can be derived by this second master equation, and the chain rule for partial derivatives.^[5]

Derivation

Starting from the equation

dG=-SdT+Vdp={\frac {\partial G}{\partial T}}dT+{\frac {\partial G}{\partial p}}dp\,\!

at constant pressure meaning dp = 0. Then dG reduces to

dG_{p}=-SdT=\left({\frac {\partial G}{\partial T}}\right)_{p}dT\quad \rightarrow \quad -S=\left({\frac {\partial G}{\partial T}}\right)_{p}.\,\!

The dependence of the ratio G/T on T is found by the product rule of differentiation:

\left({\frac {\partial (G/T)}{\partial T}}\right)_{p}={\frac {1}{T}}\left({\frac {\partial G}{\partial T}}\right)_{p}+G{\frac {\partial (T^{-1})}{\partial T}}={\dfrac {T\left({\dfrac {\partial G}{\partial T}}\right)_{p}-G}{T^{2}}}={\frac {-ST-G}{T^{2}}}=-{\frac {H}{T^{2}}}\,\!

Sources

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External links

Link - Gibbs–Helmholtz equation
Link - Gibbs–Helmholtz equation

Warning: Default sort key "Gibbs-Helmholtz equation" overrides earlier default sort key "Aharonov-Casher effect".

↑ Physical chemistry, P.W. Atkins, Oxford University Press, 1978, ISBN 0-19-855148-7
↑ Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, ISBN 0-356-03736-3
↑ Chemistry, Matter, and the Universe, R.E. Dickerson, I. Geis, W.A. Benjamin Inc. (USA), 1976, ISBN 0-19-855148-7
↑ Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, ISBN 0-356-03736-3
↑ physical chemistry, p.W. Atkins, Oxford University press, 1978, ISBN 0-19-855148-7

[1] Physical chemistry, P.W. Atkins, Oxford University Press, 1978, ISBN 0-19-855148-7

[2] Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, ISBN 0-356-03736-3

[3] Chemistry, Matter, and the Universe, R.E. Dickerson, I. Geis, W.A. Benjamin Inc. (USA), 1976, ISBN 0-19-855148-7

[4] Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, ISBN 0-356-03736-3

[5] ysical chemistry, p.W. Atkins, Oxford University press, 1978, ISBN 0-19-855148-7

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-To do which we want to do 30-45 minutes of moderate cardio (because in, sweaty-I'm-going-to-look-good-in-that-bikini-cardio) 3-5x a week. If you get bored found on the treadmill try biking, rollerblading, a dance class, or kickboxing class. The objective is to get a heart rate up for 20+ minutes.<br><br>I understand what you're thinking....."There's no technique [http://safedietplansforwomen.com/bmr-calculator bmr calculator] I could drink which much water!" However rest assured, you are able to, and the body can thank we for it. At first, we will spend a lot of time in the bathroom. But inside regarding 2 weeks, the body is fully hydrated and a bathroom breaks will level off. During those first limited weeks of frequent pit stops, only think of it because piece of your exercise system. Consider all the squats you're doing, plus if you wear clothing like overalls, you'll be getting some superior stretching in because you pull them on plus off!<br><br>Drinking water furthermore increases your basal metabolic rate. The body has to process the water, plus in doing this burns additional calories. Studies furthermore show that drinking cold water burns more calories because your body initially has to bring the water as much as your internal temperature.<br><br>It is easy to find should you want iodine. First, its a superior idea to test yourself using liquid iodine. Simply paint a round patch on the belly and observe to find how extended a body takes to absorb it. If it really is gone in a few hours, then you should supplement.<br><br>Next add the calories needed for a particular exercise you will be doing for which day to a bmr. For example a woman that weighs 165 pounds at 5'9", demands 1650 calories for BMR (body weight X 10). Let's say she is moderately active thus add another 40% to her BMR: 1650 X .40 (40%) = 660 thus 1650 + 660 = 2310.<br><br>The BMI Calculator or BMI is a helpful tool, nevertheless, it's based on weight plus does not measure fat vs muscle. There may be a number of individuals whose BMI is okay, yet have nevertheless have too much fat due to a loss of muscle when you reach this age group. So, one suggested idea is to consider your waist to cool ratio. Measuring the waistline initially, as a guide ladies must be 32inches (80cm) or less and men ought to be 37inches (94cm) or less. Anything over signifies you're at a high risk of diabetes plus heart disease. Now measure a hips and split your waist measurement by a cool measuring. Guys you need to be no higher than 0.9, ladies no high than 0.8.<br><br>Finally, on a healthy eating program, we should allow oneself 1 or two "cheats" per week. By doing so, you are able to talk oneself down from offering in whenever temptation suddenly arises. You must consult the food pyramid plus the FDA's dietary policies and never go below 500 calories lower than the body demands each day (unless a doctor provides you the ok to go lower than that).
+The '''Gibbs–Helmholtz equation''' is a [[thermodynamics|thermodynamic]] [[equation]] useful for calculating changes in the [[Gibbs energy]] of a system as a function of [[temperature]]. It is named after [[Josiah Willard Gibbs]] and [[Hermann von Helmholtz]].
+==Equation==
+The equation is:<ref>Physical chemistry, P.W. Atkins, Oxford University Press, 1978, ISBN 0-19-855148-7</ref>
+{{Equation box 1
+|indent =:
+|equation = <math>\left( \frac{\partial (G/T) } {\partial T} \right)_p = - \frac {H} {T^2}</math>
+|cellpadding
+|border
+|border colour = #50C878
+|background colour = #ECFCF4}}
+where ''H'' is the [[enthalpy]], ''T'' the [[absolute temperature]] and ''G'' the [[Gibbs free energy]] of the system, all at constant [[pressure]] ''p''. The equation states that the change in the ''G/T'' ratio at constant pressure as a result of an infinitesimally small change in temperature is a factor ''H/T''<sup>2</sup>.
+==Chemical reactions==
+{{Main|Thermochemistry}}
+The typical applications are to [[chemical reaction]]s. The equation reads:<ref>Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, ISBN 0-356-03736-3</ref>
+:<math>\left( \frac{\partial ( \Delta G^\ominus/T ) } {\partial T} \right)_p = - \frac {\Delta H} {T^2}</math>
+with Δ''G'' as the change in Gibbs energy and Δ''H'' as the enthalpy change (considered independent of temperature). The <s>o</s> denotes [[Standard conditions for temperature and pressure]] (approximately temperature 298.15 [[Kelvin]] and pressure 101,325 [[pascal (unit)|pascal]]s).
+Integrating with respect to ''T'' (again ''p'' is constant) it becomes:
+:<math> \frac{\Delta G^\ominus(T_2)}{T_2} - \frac{\Delta G^\ominus(T_1)}{T_1} = \Delta H^\ominus(p)\left(\frac{1}{T_2} - \frac{1}{T_1}\right) </math>
+This equation quickly enables the calculation of the Gibbs free energy change for a chemical reaction at any temperature ''T''<sub>2</sub> with knowledge of just the [[Standard Gibbs free energy change of formation]] and the [[Standard enthalpy change of formation]] for the individual components.
+Also, using the reaction isotherm equation,<ref>Chemistry, Matter, and the Universe, R.E. Dickerson, I. Geis, W.A. Benjamin Inc. (USA), 1976, ISBN 0-19-855148-7</ref> that is
+:<math>\frac{\Delta G^\ominus}{T} = -R \ln K </math>
+which relates the Gibbs energy to a chemical [[equilibrium constant]], the [[van 't Hoff equation]] can be derived.<ref>Chemical Thermodynamics, D.J.G. Ives, University Chemistry, Macdonald Technical and Scientific, 1971, ISBN 0-356-03736-3</ref>
+==Derivation==
+===Background===
+{{main|Defining equation (physical chemistry)|Enthalpy|Thermodynamic potential}}
+The definition of the Gibbs function is
+:<math>H= G + ST \,\!</math>
+where ''H'' is the enthalpy defined by:
+:<math>H= U + pV \,\!</math>
+Taking [[differential of a function|differentials]] of each definition to find ''dH'' and ''dG'', then using the [[fundamental thermodynamic relation]], aka "master equation" (always true for [[Reversible process (thermodynamics)|reversible]] or [[Irreversible process|irreversible]] [[thermodynamic process|processes]]):
+:<math>dU= TdS - pdV \,\!</math>
+where ''S'' is the [[entropy]], ''V'' is [[volume]], (minus sign due to reversibility, in which ''dU'' = 0: work other than pressure-volume may be done and is equal to −''pV'') leads to the "reversed" form of the initial fundamental relation into a new master equation:
+:<math>dG= - SdT + Vdp \,\!</math>
+This is the [[Gibbs free energy]] for a closed system. The Gibbs–Helmholtz equation can be derived by this second master equation, and the [[chain rule]] for [[partial derivatives]].<ref>physical chemistry, p.W. Atkins, Oxford University press, 1978, ISBN 0-19-855148-7</ref>
+:{| class="toccolours collapsible collapsed" width="80%" style="text-align:left"
+!Derivation
+|-
+|Starting from the equation
+:<math>dG =  - SdT + Vdp = \frac{\partial G}{\partial T}dT + \frac{\partial G}{\partial p}dp \,\!</math>
+at constant [[pressure]] meaning ''dp'' = 0. Then ''dG'' reduces to
+:<math>dG_p =  - SdT = \left(\frac{\partial G}{\partial T}\right)_p dT \quad \rightarrow \quad -S = \left(\frac{\partial G}{\partial T}\right)_p. \,\!</math>
+The dependence of the ratio ''G/T'' on ''T'' is found by the [[product rule]] of [[Differentiation (mathematics)|differentiation]]:
+:<math>\left( \frac{\partial(G/T)} {\partial T} \right)_p = \frac{1}{T}\left(\frac{\partial G}{\partial T}\right)_p + G\frac{\partial (T^{-1})}{\partial T} = \dfrac{T\left ( \dfrac{\partial G}{\partial T} \right)_p- G}{T^2} = \frac{-ST - G}{T^2} = -\frac{H}{T^2} \,\!</math>
+|}
+==Sources==
+{{reflist}}
+==External links==
+* [http://www.chem.arizona.edu/~salzmanr/480a/480ants/gibshelm/gibshelm.html Link] - Gibbs–Helmholtz equation
+* [http://www.owlnet.rice.edu/~chem312/Handouts%20Folder/Gibbs_Helmholtz.pdf Link] - Gibbs–Helmholtz equation
+{{DEFAULTSORT:Gibbs-Helmholtz equation}}
+[[Category:Thermodynamic equations]]
+[[Category:Equations]]

Call option: Difference between revisions

Revision as of 22:06, 4 January 2014

Contents

Equation

Bibliography

See also

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Call option: Difference between revisions

Revision as of 22:06, 4 January 2014

Equation

Bibliography

See also

Chemical reactions

Derivation

Background

Sources

External links

Navigation menu

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