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

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Chemical Engineering Thermodynamics
It is desired to bring about a certain change in the state of a system by performing work on the system under adiabatic conditions.

The amount of work needed is independent of path
The amount of work needed is path dependent
More information is needed to conclude anything about the path dependence or otherwise of the work needed
Work alone can not bring out such a change of state

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