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) )?

Question

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

Share with your friends

Talk Doctor Online in Bissoy App

AhmedNazir · Answer 1 · Sep 01, 2022 13:21:41

Answer: Option 3

For an adiabatic process → $$P{V^y}$$ = constant For an isothermal process → $$PV$$ = constant So, slope for adiabatic process in $$PV$$ plane is $$\frac{{dp}}{{dv}} = - y\frac{p}{v}$$ Slope for isothermal process is $$\frac{{dp}}{{dv}} = - \frac{p}{v}$$ Hence, $${\left( {\frac{{\partial p}}{{\partial v}}} \right)_S} = - y{\left( {\frac{{\partial p}}{{\partial v}}} \right)_T}$$

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) )?

1 Answers