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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 = â€“SdT + VdP

dA = â€“PdV â€“ SdT

dV = TdS â€“ PdV

dA = (â€“P)dV + (â€“S)dT

dA = â€“PdV â€“ SdT â€¦(3)

dG = VdP + (â€“S)dT

dG = VdP â€“ SdT â€¦(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 Eulerâ€™s theorem.

We know that if z s the funct ion of x & y then z = f(x, y)

â‡’

if z is state funct ion then it follow the Eulerâ€™s theorem

i.e.

â‡’

Four Maxwell thermodynamic equation is are given below:

dH = TdS + VdP

dG = VdP â€“ SdT

dA = â€“PdV â€“ SdT

dV = TdS â€“ PdV

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

dH = TdS + VdP

â‡’

i.e.

dG = VdP â€“ SdT

â‡’

dA = â€“PdV â€“ SdT

â‡’

i.e.

dV = TdS â€“ PdV

â‡’

** 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.

â€œThe variation of volume V with temperature T, keeping pressure P constant is called the coefficient of thermal expansion or expansivity. It is denoted by Î±. Thus

Similarly â€œthe variat ion of V with P, keeping T constant, is called the coefficient of isothermal compressibility or compressibility. It is denoted by Î²

Another coefficient, isochoric thermal expansion coefficient, when the variation of P with T, keeping V constant is represented by Î³

**Problem. Find the value of Î±, Î², Î³**** for ideal gas?****Sol.** Ideal gas equation is

PV = nRT (for n mole)

PV = RT (for 1 mole)

for ideal gas

PV = nRT

â‡’

â‡’

â‡’ â€¦(1)

for ideal gas

PV = nRT

PV = nRT

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