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 = C_p/C_v)

Question

A. (∂P/∂V)_S = (∂P/∂V)_T

B. (∂P/∂V)_S = [(∂P/∂V)_T]^Y

C. (∂P/∂V)_S = y(∂P/∂V)_T

D. (∂P/∂V)_S = 1/y(∂P/∂V)_T

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Accepted Answer

C. (∂P/∂V)_S = y(∂P/∂V)_T

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)