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]
Free AP Physics Study Guide, AP Physics Test Papers, AP Physics Practice papers, AP Physics Test pattern and general information, Find AP Physics exam information and resource, material free at Tutorsglobe.com
tutorsglobe.com demand schedule and demand curve assignment help-homework help by online theory of demand tutors
General ledger is the support of any accounting system that holds financial and non-financial data for an organization.
Theory and lecture notes of Transaction scheduling all along with the key concepts of transaction scheduling, transaction management, Primed transactions. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Transaction scheduling.
washing technique used in washing machines are pulsator technique, agitators wash technique, tumbler washing tub technique.
the electron ray begins to scan from line one and follow constantly (trace line and retrace line) making full scanning of 15625 in a second is termed as progressive scanning.
tutorsglobe.com digestion of lipids assignment help-homework help by online digestion tutors
Sequencing of Peptide tutorial all along with the key concepts of sequencing peptides and proteins, Steps to Sequencing, Deciphering the Complete Primary Structure
The Valence Bond Theory tutorial all along with the key concepts of Hybridisation of Atomic Orbitals, sp Hybrid Atomic Orbitals, sp2 Hybrid Orbitals, sp3 Hybrid Orbitals, Molecular Shapes of Compounds
We promise impeccable Professional Ethics Assignment Help service at reasonable rates to enhance your academic grades.
tutorsglobe.com mechanism of fission assignment help-homework help by online type of nuclear reaction tutors
tutorsglobe.com techniques of immunofluorescence assignment help-homework help by online antigen antibody reactions tutors
tutorsglobe.com characteristics of capital assignment help-homework help by online capital tutors
Hierarchical organization tutorial all along with the key concepts of Definition of hierarchical organization, Visualization, Hierarchiology, Studies of hierarchical organizations, Criticism and Alternatives, Dominance Hierarchies and Effects of Dominance Hierarchy
Avail 100% unique & plagiarism free Ageing and Health Assignment Help by industry best tutors for achieving great academic success!
1951680
Questions Asked
3689
Tutors
1455190
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!