Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

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Thermodynamic Magic Square

Magic square play a very important role in thermodynamic. By using magic square we find many important relat ionships between thermodynamic funct ion or quant it y. These relations 

Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

are known as Maxwell thermodynamic equation. S, P, V, T are at the corner of square & known as thermodynamic coordinates.
We can find the Maxwell thermodynamic equation by using magic square.
dH = TdS + VdP
dG = –SdT + VdP
dA = –PdV – SdT
dV = TdS – PdV 

 Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

dA = (–P)dV + (–S)dT
dA = –PdV – SdT …(3)
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev 

dG = VdP + (–S)dT
dG = VdP – SdT …(4) i.e.,

we can find the Maxwell thermodynamic equation by using magic square.

Maxwell relationship between thermodynamic coordinate.
i.e., S, P, V, T. 

 Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev                     Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev..........(2)
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev                        Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev..............(3)
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev                          Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev ................(4)

We can find the relation between thermodynamic coordinate by using Euler’s theorem.
We know that if z s the funct ion of x & y then z = f(x, y)

Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

if z is state funct ion then it follow the Euler’s theorem 
i.e.    Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

⇒ Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

Four Maxwell thermodynamic equation is are given below:
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
dH = TdS + VdP
dG = VdP – SdT
dA = –PdV – SdT
dV = TdS – PdV

We know that H, G, A & V are state funct ion i.e., it fo llow the Euler’s theorem.

dH = TdS + VdP


i.e.    Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

dG = VdP – SdT
⇒ Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

dA = –PdV – SdT
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
i.e.Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

dV = TdS – PdV
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

 Expansivity and compressibility:
Gas expands on heating through 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

 Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

Similarly “the variat ion of V with P, keeping T constant, is called the coefficient of isothermal compressibility or compressibility. It is denoted by β

 Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

Another coefficient, isochoric thermal expansion coefficient, when the variation of P with T, keeping V constant is represented by γ

 Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

Problem.  Find the value of α, β, γ for ideal gas?
Sol. Ideal gas equation is
PV = nRT         (for n mole)

PV = RT           (for 1 mole)

 Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev         for ideal gas

PV = nRT

Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev …(1)

 Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

 Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev  for ideal gas

PV = nRT

 Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

 Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

PV = nRT
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev
Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

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