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# Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev

## Physical Chemistry

Created by: Asf Institute

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

The document Thermodynamic Magic Square - Thermodynamic Chemistry Notes | EduRev is a part of the Chemistry Course Physical Chemistry.
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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 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   dA = (–P)dV + (–S)dT
dA = –PdV – SdT …(3) 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.   ..........(2)  ..............(3)  ................(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) if z is state funct ion then it follow the Euler’s theorem
i.e. ⇒ Four Maxwell thermodynamic equation is are given below: 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. dG = VdP – SdT
⇒ dA = –PdV – SdT i.e. dV = TdS – PdV 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 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 Another coefficient, isochoric thermal expansion coefficient, when the variation of P with T, keeping V constant is represented by γ 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)  for ideal gas

PV = nRT   …(1)   for ideal gas

PV = nRT       PV = nRT     Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

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