A fixed amount of a real gas is compressed isothermally at a temperature below its Boyle temperature. Which statements about the compressibility factor $Z$ are correct?

A $Z$ passes through a minimum and then rises above 1
BThe minimum in $Z$ becomes shallower as the temperature is raised
CAt the pressure where $Z = 1$ (after the minimum) the gas behaves ideally in every respect
DAt very high pressure $Z$ exceeds 1 because the molecular volume is no longer negligible

Answer: A, B, D

Below

T_{B}

attractions dominate at low pressure so

Z

dips, then repulsions dominate so

Z

rises above 1 (A true). Raising

T

reduces

a / RT

and the dip becomes shallower until it vanishes at

T_{B}

(B true). At the crossing point

Z = 1

only because the attractive and repulsive corrections happen to cancel; the slope

d Z / d P

is not zero and other properties are not ideal (C false). At high pressure the excluded volume dominates (D true).