A real gas is described by Z = 1 + (P)/(RT)(b - (a)/(RT)) at low pressure. Which statements follow from this expression?

(partial Z/partial P)_T at low pressure is (1)/(RT)(b - (a)/(RT))

The initial slope of Z versus P is zero at T = a/Rb

At very high temperature the initial slope approaches b/RT, a positive value

(partial Z/partial P)_T at low pressure is (1)/(RT)(b - (a)/(RT))

The initial slope of Z versus P is zero at T = a/Rb

At very high temperature the initial slope approaches b/RT, a positive value

At very high temperature the initial slope approaches zero from below

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3rg120

A real gas is described by $Z = 1 + \frac{P}{RT} (b - \frac{a}{RT})$ at low pressure. Which statements follow from this expression?

A $(\partial Z / \partial P)_{T}$ at low pressure is $\frac{1}{RT} (b - \frac{a}{RT})$
BThe initial slope of $Z$ versus $P$ is zero at $T = a / R b$
CAt very high temperature the initial slope approaches $b / RT$ , a positive value
DAt very high temperature the initial slope approaches zero from below

Differentiating with respect to

P

gives the stated slope (A true). It vanishes when

b = a / RT

, i.e.

T = a / R b = T_{B}

(B true). As

T \to \infty

the term

a / RT

vanishes faster than

b

, so the slope tends to

b / RT

, positive and decreasing toward zero from above (C true, D false).