Differential forms of thermodynamic potentials are:
dU = TdS - PdV
dH =TdS +VdP
dA= - SdT - PdV
dG = - SdT +VdP
Four Maxwell relations are derived from each of these four thermodynamic potentials.
1st Relation:
Differential form of internal energy U is:
Differentiating this with respect to S whereas V is kept constant gives:
(∂U/∂S)V = T and with respect to V whereas S is kept constant gives:
(∂U/∂V)S = -P
Also differentiating given equations with respect to V at constant S and with respect to S at constant V respectively will provide:
∂2U/∂V∂S = (∂T/∂V) S and ∂2U/∂S∂V = - (∂P/∂S)V
Mixed second order derivatives of U that means:
(∂T/∂V)S = - (∂P/∂S)V
This equation is one of the four Maxwell relations.
2nd Relation:
From differential form of Enthalpy H (i.e. dH = TdS +VdP)
(∂H/∂S)P = T and (∂H/∂P)S = P
Second derivative provides:
(∂2H/∂P∂S) = (∂T/∂P)S and ∂2H/∂S∂P = (∂P/∂S)P
Mixed second order derivatives of H are equal, therefore:
(∂T/∂P)S = (∂P/∂S)P
This equation is one of four Maxwell's relations.
3rd Relation:
From differential of Helmholtz free energy A (i.e. dA = - SdT - PdV)
(∂A/∂T)V = -S and (∂A/∂V)T = -P
(∂2A/∂V∂T) = - (∂S/∂V)T and ∂2A/∂T∂V = - (∂P/∂T)V
Mixed second derivatives of A are equal, hence
- (∂S/∂V)T = - (∂P/∂T)V i.e. (∂S/∂V)T = (∂P/∂T)V
(∂P/∂T)V in equation can be achieved from equation of state. This means that variation of entropy S with respect to volume V at constant temperature T for the system can be achieved from equation of state for system.
4th Relation:
From differential of Gibb's free energy G (i.e. dG = - SdT +VdP), partial derivative provides
(∂G/∂T)P = -S and (∂G/∂P)T = V
Differentiating both equations with respect to P at constant T, and with respect to T at constant P respectively provide
(∂2G/∂P∂T)P = - (∂S/∂P)T and (∂2G/∂T∂P) = (∂V/∂T)P respectively.
Mixed second derivatives of G are equal, therefore
(∂S/∂P)T = - (∂V/∂T)P
(∂V/∂T)P in given equation can be attained from equation of state.
Maxwell Relations:
Four Maxwell Relations of thermodynamics are given below:
(∂S/∂V)T = (∂P/∂T)V
Usefulness:
These relations (that is Maxwell relations) are helpful in thermodynamics calculations. For instance, one can replace the derivative of entropy with the derivative of simple thermodynamic variation like temperature. Equations give derivative of entropy in terms of temperature T, volume V and pressure P.
(∂S/∂V)T = (∂P/∂T)V and (∂S/∂P)T = - (∂V/∂T)P
For the ideal gas, PV = nRT
(∂P/∂T)V = nR/V = P/T and (∂V/∂T)P = nR/P = V/T
For the ideal gas, equation becomes:
(∂S/∂V)T = P/T
(∂S/∂P)T = -V/T
Tutorsglobe: A way to secure high grade in your curriculum (Online Tutoring)
Expand your confidence, grow study skills and improve your grades.
Since 2009, Tutorsglobe has proactively helped millions of students to get better grades in school, college or university and score well in competitive tests with live, one-on-one online tutoring.
Using an advanced developed tutoring system providing little or no wait time, the students are connected on-demand with a tutor at www.tutorsglobe.com. Students work one-on-one, in real-time with a tutor, communicating and studying using a virtual whiteboard technology. Scientific and mathematical notation, symbols, geometric figures, graphing and freehand drawing can be rendered quickly and easily in the advanced whiteboard.
Free to know our price and packages for online physics tutoring. Chat with us or submit request at [email protected]
Principles of segregation tutorial all along with the key concepts of Mendel's First Law, Punnett Squares, Locus, Homozygous or Heterozygous, Phenotypic Ratio, Genotypic Ratio and Monohybrid Cross
www.tutorsglobe.com offers incremental model homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
tutorsglobe.com energy crisis assignment help-homework help by online energy crisis and its environmental impact tutors
are assignments giving you nightmares? get best accounting for fixed assets assignment help and attain a++ and make it a sweet dream.
grab the chance to score maximum grades with superb electrical engineering assignment help at reasonable price range.
electronic transfer tutorial all along with the key concepts of drude model, origin of collision time, thermal conductivity, motion in a magnetic field, cyclotron resonance and hall effect
tutorsglobe.com angina pectoris assignment help-homework help by online circulation tutors
tutorsglobe.com q,r, and s waves assignment help-homework help by online ecg-electrocardiogram tutors
Vegetative Structure of Seed Plants-Stem tutorial all along with the key concepts of Major functions of stems, Stem Structure, Dicot stems, Gymnosperm stems and Economic significance of Stems
There is a unique adjustment for every channel. Resonance is acquired with coil’s distributed capacitance, stray and trimmer capacitors. The oscillator coil is generally constructed with an aluminium or brass screw as the core for fine tuning.
www.tutorsglobe.com offers cohesion homework help, assignment help, case study, writing homework help, online tutoring assistance by computer science tutors.
tutorsglobe.com lens replacement assignment help-homework help by online receptor organs tutors
theory and lecture notes of static characteristics iv, all along with the key concepts of drive capability, fan-out, assignment help and homework help. tutorsglobe offers homework help, assignment help and tutor’s assistance on static characteristics iv.
Radio analytical separation techniques tutorial all along with the key concepts of Precipitation, Distillation, Solvent Extraction, Ion Exchange and Electrochemical deposition
the material control is guaranteed through laying down proper methods for storing, purchasing, issuing and minimizing material losses through identifying slow moving, obsolete, dormant material and also through minimizing scrap, wastages, spoilages and defectives.
1952312
Questions Asked
3689
Tutors
1480296
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!