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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]].
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==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]]

Revision as of 21:38, 27 February 2014

If you think of oneself as being fat and ugly then this might be the right spot for we. In this short article there is a step-by-step representation of Ways to Lose fat. For many weight reduction can confirm to be a extremely difficult problem to deal with due to the truth that they just do not have the idea of how to burn the calories and what to avoid plus what to consume that might supply the nourishment without piling up the calories.

To lose weight fast plus easy change what we drink, I've seenpeople inside terrible bodily shape who wouldn't drink anythingexcept diet coke. If you like to lose fat yet you won't stopdrinking pop then leave this page because you're spending yourtime.

Diet Plan: It is important that you have right diet meal program that could assist we lower weight faster. Ensure which you follow a low carb, low fat and high protein diet. You must eat at fixed times daily which may help we lose weight quicker. We should keep a diary which has an account of what you have consumed throughout the day. A glance at which diary assists we check a progress or shortcomings.

Have we any idea how much of the weight derives from fat, plus how much stems from muscle? If not, you need to use calipers or an electronic body fat calculator to obtain out. If you require guidance, talk with an expert inside nutrition, fitness instructor, or your health provider.

Everyone want to understand lose weight plus it's possible to lose it rapidly using medications but these have bad side effects. It's also possible to starve oneself by going on among the diets which cuts out food all together plus to get rid of weight rapidly. You may have observed which most of those who do lose weight this method place it all back on again.

Ever question why Brazilians are perpetually slim? They appear to enjoy their traditional dish so much that they have it with only about every meal. The dish consists of rice and beans which lowers the risk of gaining excess weight. The dish is high in fiber plus low inside fat. Hence, the blood sugar degrees are stabilized plus a beach-ready body is the final result. On the different hand, eating breakfast is a daily habit of 75 % of Germans. Breakfast means whole-grain cereals, fruit and breads. Skipping breakfast has always been advised against by all nutritionists. So in the event you are into losing pounds, we should eat breakfast like the Germans.

Always make certain that we spend 5 or 10 minutes warming up gradually as this gives the body a gentle nudge to wake itself up. I promise we which after a short time of carrying this out we will start to feel desirable everyday. Look at professional boxers, from the early days of boxing up till the present day, boxers have woken up inside the early hours to run. Boxers are certain of the many physically fit specimens of human beings which you can come across. If they usually do cardio in the mornings, surely which is enough to tell we it is advantageous should you may exercise early to get rid of fat.

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