Chemical Engineering Thermodynamics
On a P-V diagram of an ideal gas, suppose a reversible adiabatic line intersects a reversible isothermal line at point A. Then at a point A, the slope of the reversible adiabatic line (∂P/∂V)S and the slope of the reversible isothermal line (∂P/∂V)T are related as (where, y = Cp/Cv) )

(∂P/∂V)S = y(∂P/∂V)T
(∂P/∂V)S = 1/y(∂P/∂V)T
(∂P/∂V)S = (∂P/∂V)T
(∂P/∂V)S = [(∂P/∂V)T]Y

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Chemical Engineering Thermodynamics
Law of corresponding states says that

No gas can be liquified above the critical temperature, howsoever high the pressure may be
, two different gases behave similarly, if their reduced properties (i.e. P, V and T) are same
The surface of separation (i. e. the meniscus) between liquid and vapour phase disappears at the critical temperature
The molar heat of energy of gas at constant volume should be nearly constant (about 3 calories)

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