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 importance of the law assignment help-homework help by online equi-marginal utility tutors
tutorsglobe.com sexual reproduction assignment help-homework help by online bacteria tutors
TutorsGlobe.com Introduction to Polymer Chemistry Assignment Help-Homework Help by Online Access Chemistry Tutors
tutorsglobe.com rainwater harvesting from tiled roofs assignment help-homework help by online collection of rainwater from terrace tutors
tutorsglobe.com aids assignment help-homework help by online microbiology tutors
tutorsglobe.com nitrogen cycle assignment help-homework help by online biogeochemical cycle tutors
global weather and climatic patterns tutorial all along with the key concepts of components of the earth, energy cycle, terrestrial atmosphere, weather and landform, greenhouse effect, ozone layer depletion, environmental management, environmental modeling, environmental cost-benefit analysis
Forms of Carbohydrates tutorial all along with the key concepts of Importance of Carbohydrates, Classification of Carbohydrates, Ketoses, Anomeric Forms of Glucose and Cyclic Forms of Sugars
www.tutorsglobe.com offers the hückel's rule homework help, the hückel's rule assignment help, online tutoring assistance, organic chemistry solutions by online qualified tutor's help.
Theory and lecture notes of Transistor Inverter Applications II, all along with the key concepts of Relay Driving Circuit, Steps for finding Relay driving and Assignment help. Tutorsglobe offers homework help, assignment help and tutor’s assistance on Transistor Inverter Applications II.
There are two issues that can be taken to preparing the statement of cash flows: the direct method and the indirect method.
After than the lifting out the core and placing it upon a trestle, the interior of the tank should be carefully cleaned of all accumulated muck, sludge, and dirt.
tutorsglobe.com immunological basis of graft rejection assignment help-homework help by online tissue transplantation tutors
theory and lecture notes of dynamic characteristics iv, all along with the key concepts of effect of capacitive loading, transistor turn-off, transistor turn-on and laplace transform. tutorsglobe offers homework help, assignment help and tutor’s assistance on dynamic characteristics iv.
the various types of classification proposed through earlier taxonomists can be generally categorized into three systems– artificial, natural and phylogenetic.
1943608
Questions Asked
3689
Tutors
1472665
Questions Answered
Start Excelling in your courses, Ask an Expert and get answers for your homework and assignments!!