Gibbs energy function: Difference between revisions
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:<math>\left.G\right.=A+pV</math> | :<math>\left.G\right.=A+pV</math> | ||
where ''p'' is the [[pressure]], ''V'' is the volume, and ''A'' is the [[Helmholtz energy function]], i.e. | |||
:<math>\left.G\right.=U-TS+pV</math> | :<math>\left.G\right.=U-TS+pV</math> | ||
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thus one arrives at | thus one arrives at | ||
:<math>\left.dG\right.=-SdT+Vdp</math> | |||
<math>\left.dG\right.=-SdT+Vdp</math> | |||
For ''G(T,p)'' we have the following ''total differential'' | For ''G(T,p)'' we have the following ''total differential'' | ||
:<math>dG=\left(\frac{\partial G}{\partial T}\right)_p dT + \left(\frac{\partial G}{\partial p}\right)_T dp</math> | :<math>dG=\left(\frac{\partial G}{\partial T}\right)_p dT + \left(\frac{\partial G}{\partial p}\right)_T dp</math> | ||
[[Category: Classical thermodynamics]] | |||
Latest revision as of 17:17, 29 January 2008
Definition:
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left.G\right.=A+pV}
where p is the pressure, V is the volume, and A is the Helmholtz energy function, i.e.
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left.G\right.=U-TS+pV}
Taking the total derivative
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left.dG\right.=dU-TdS-SdT+pdV+Vdp}
From the Second law of thermodynamics one obtains
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left.dG\right.=TdS -pdV-TdS-SdT+pdV+Vdp}
thus one arrives at
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left.dG\right.=-SdT+Vdp}
For G(T,p) we have the following total differential
- Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle dG=\left(\frac{\partial G}{\partial T}\right)_p dT + \left(\frac{\partial G}{\partial p}\right)_T dp}