In thermodynamics, the Maxwell equations are a set of equations derived by application of Euler's reciprocity relation to the thermodynamic characteristic functions.
The Maxwell relations, first derived by James Clerk Maxwell, are the following expressions:
The magic square plays a very important role in thermodynamic. By using magic square we find many important relationships between thermodynamic function or quantity.
These relations are known as Maxwell thermodynamic equations. S, P, V, T are at the corner of the square & known as thermodynamic coordinates.
We can find the Maxwell thermodynamic equation by using magic square.
dA = (–P)dV + (–S)dT
dA = –PdV – SdT …(3)
dG = VdP + (–S)dT
dG = VdP – SdT …(4) i.e.,
![]() |
Test: Thermodynamics And Thermochemistry - 1
|
Start Test |
we can find the Maxwell thermodynamic equation by using magic square.
..........(2)
..............(3)
................(4)
We can find the relation between thermodynamic coordinates by using Euler’s theorem.
We know that if z s the function of x & y then z = f(x, y)
⇒
if z is a state function then it follows Euler’s theorem
i.e.
⇒
Four Maxwell thermodynamic equation are given below:
dH = TdS + VdP
dG = VdP – SdT
dA = –PdV – SdT
dV = TdS – PdV
We know that H, G, A & V are state function i.e., it follow the Euler’s theorem.
dH = TdS + VdP
⇒
i.e.
dG = VdP – SdT
⇒
dA = –PdV – SdT
⇒
i.e.
dV = TdS – PdV
⇒
![]() |
Download the notes
Thermodynamic Magic Square
|
Download as PDF |
The gas expands on heating through the expansion of gases is much more than that of liquids. Similar gas compressed on increasing the pressure.
“The variation of volume V with temperature T, keeping pressure P constant is called the coefficient of thermal expansion or expansivity. It is denoted by α. Thus
Similarly “the variation of V with P, keeping T constant, is called the coefficient of isothermal compressibility or compressibility. It is denoted by β
Another coefficient, isochoric thermal expansion coefficient, when the variation of P with T, keeping V constant is represented by γ
Q.1. Find the value of α, β, γ for an ideal gas?
Sol. Ideal gas equation is
PV = nRT (for n mole)
PV = RT (for 1 mole)
for ideal gas
PV = nRT
⇒
⇒
⇒ …(1)
for ideal gas
PV = nRT
PV = nRT
83 videos|142 docs|67 tests
|
1. What are Maxwell's thermodynamic equations? | ![]() |
2. What is the thermodynamic magic square? | ![]() |
3. What is expansivity in thermodynamics? | ![]() |
4. What is compressibility in thermodynamics? | ![]() |
5. How are the thermodynamic magic square and Maxwell's equations useful in practical applications? | ![]() |