The isotherms of a van der Waals gas are plotted as $P$ against $V_{m}$ . Which statements are correct?

AFor $T$ less than $T_{c}$ each isotherm has a maximum and a minimum
BFor $T$ greater than $T_{c}$ the isotherms are monotonic
CAt $T = T_{c}$ the isotherm has a point of inflection with a horizontal tangent
DThe region between the maximum and minimum of a sub-critical isotherm, where $P$ increases with $V_{m}$ , is physically stable

Answer: A, B, C

Below

T_{c}

the cubic equation gives an S-shaped loop with a local maximum and minimum (A true). Above

T_{c}

the isotherm falls monotonically like an ideal gas (B true). The critical isotherm has

(\partial P / \partial V_{m})_{T} = 0

and

(\partial^{2} P / \partial V_{m}^{2})_{T} = 0

at the critical point (C true). A region where

P

rises with

V_{m}

has negative compressibility and is mechanically unstable; it is replaced in reality by the horizontal two-phase line (D false).