The relation PV = nRT holds for all ideal gases. The additional relation PVγ holds for an adiabatic process. The figure below shows two curves: one is an adiabat and one is an isotherm. Each starts at the same pressure and volume. Which statement is correct? (Note: "∝" means "is proportional to".)
A) Isotherm: ; Adiabat: : A is both an isotherm and an adiabat.
B) Isotherm: ; Adiabat: : B is an isotherm, A is an adiabat.
C) Isotherm: ; Adiabat: : A is an isotherm, B is an adiabat.
D) Isotherm: ; Adiabat: : B is both an isotherm and an adiabat.
E) cannot answer without additional information about the starting temperature.

Question

The relation PV = nRT holds for all ideal gases. The additional relation PVγ holds for an adiabatic process. The figure below shows two curves: one is an adiabat and one is an isotherm. Each starts at the same pressure and volume. Which statement is correct? (Note: "∝" means "is proportional to".) 
A) Isotherm: ; Adiabat: : A is both an isotherm and an adiabat. 
B) Isotherm: ; Adiabat: : B is an isotherm, A is an adiabat. 
C) Isotherm: ; Adiabat: : A is an isotherm, B is an adiabat. 
D) Isotherm: ; Adiabat: : B is both an isotherm and an adiabat. 
E) cannot answer without additional information about the starting temperature.

Quizplus · Accepted Answer

The question states that both the adiabat and the isotherm start at the same pressure and volume. This means that their initial state is the same, and therefore, they intersect at that point. The adiabat has a steeper slope than the isotherm (PV^(γ) = constant vs PV = constant), which means that it will rise faster as the volume increases. Therefore, at some point, the adiabat will cross the isotherm again. This can only happen if the isotherm is below the adiabat at some point. From the given plots, it is clear that A is an isotherm, and B is an adiabat, so the correct choice is C.

The Relation PV = NRT Holds for All Ideal Gases