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]
tutorsglobe.com role of f0–f1 atpase assignment help-homework help by online oxidative phosphorylation tutors
tutorsglobe.com phylum coelenterate assignment help-homework help by online animal kingdom tutors
tutorsglobe.com working capital forecasts assignment help-homework help by online working capital management tutors
Get Criminal Law and Procedure Assignment Help now, as our tutors can write on any topic, within tight deadline and fetch you A++ grades!
Regulation of Output Voltage tutorial all along with the key concepts of Zener Diode Shunt Regulator, Transistor Series Voltage Regulator, Controlled Transistor Series Regulator, Transistor Shunt Voltage Regulator, Transistor Current Regulator, Variable Feedback Regulator, Basic Op-Amp Series Regulator
tutorsglobe.com income and substitution effects assignment help-homework help by online demand tutors
tutorsglobe.com endoscopy methods assignment help-homework help by online medical lab methods tutors
Animals Displaying Homosexual Behavior tutorial all along with the key concepts of Mammals, Humans, Dog, Birds, Chicken, Reptiles, Desert Tortoise and Wood Turtles
tutorsglobe.com energy crisis assignment help-homework help by online energy crisis and its environmental impact tutors
tutorsglobe.com classification of gymnosperms assignment help-homework help by online spermatophytes tutors
Boolean algebra and Flip Flops tutorial all along with the key concepts of Logic gates, AND Gate, OR Gate, NOT Gate, Combination of Logic Gates, NAND Gate, NOR gate, Boolean algebra, Boolean Theorems
Arthropoda Class-Insecta tutorial all along with the key concepts of Characteristics of Arthropoda Class Insecta, Structure of the Insect, Water Regulation in Arthropoda, Tracheal System in Arthropoda, Wings of Arthropoda, Chitin - a Limiting Agent and Insect Societies
Manufacture of Nitric acid tutorial all along with the key concepts of Manufacture of nitric acid from Chile Saltpetre, Ostwald's Process and Uses of Nitric Acid
Buffering Capacity of Amino Acids tutorial all along with the key concepts of Ionization of Water, Calculation of Hydrogen ion Concentration, Dissociation of Weak Acids, Definition of pKa, Buffer Solutions
Introduction to Inorganic Chemistry tutorial all along with the key concepts of Organic and inorganic chemistry, History of Inorganic Chemistry, Advances in inorganic chemistry and Practical applications of Inorganic chemistry
1956415
Questions Asked
3689
Tutors
1484247
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!