For any pure substance, we can construct an equation of state of the form P=P(V,T), i.e., we can consider P to be some function of two independent state variables V and T.
A) Draw a P-V plot for a van der Waals gas isotherm for some temeprature below the critical temperature Tc.
B) Draw on the same graph as accurately as you can, the isotherm for T=Tc and mark the critical point (Pc,Vc)
C) Write down two partial derivatives that are zero at the critical point(Pc,Vc,Tc)
D) Remember each isotherm on your graph is a special case of the equation of state. Write the total differential dP for the function P(T,V)
E) Now, using your expression in (d), set dP=0 and write an expression for (deltaP/deltaT)v.
F) Next simplify your expression from part (e) with commonly tabulated quantities
G) Verify your general result in (f) for the specific case of a perfect gas
For any pure substance, we can construct an equation of state of the form P=P(V,T), i.e., we can consider P to be some function of two independent state variables V and T.
A) Draw a P-V plot for a van der Waals gas isotherm for some temeprature below the critical temperature Tc.
B) Draw on the same graph as accurately as you can, the isotherm for T=Tc and mark the critical point (Pc,Vc)
C) Write down two partial derivatives that are zero at the critical point(Pc,Vc,Tc)
D) Remember each isotherm on your graph is a special case of the equation of state. Write the total differential dP for the function P(T,V)
E) Now, using your expression in (d), set dP=0 and write an expression for (deltaP/deltaT)v.
F) Next simplify your expression from part (e) with commonly tabulated quantities
G) Verify your general result in (f) for the specific case of a perfect gas
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