Discussion Forum



1)

If Z is a compressibility  factor, van der Waal's equation at low pressure can be written as 


A) $Z= 1+\frac{RT}{pb}$

B) $Z= 1-\frac{a}{VRT}$

C) $Z= 1-\frac{pb}{RT}$

D) $Z= 1+\frac{pb}{RT}$

Answer:

Option B

Explanation:

To solve this problem the stepwise approach required i.e,

 (i) write the van der Waal's equation, then apply the condition that  at low pressure, volume become high,

    i.e, V-b=V

 Now, calculate  the value of  compressibility factor (Z). [Z=pV/RT]

 According to Van der Waal's equation,

                    $\left(p+\frac{a}{V^{2}}\right)(V-b)=RT$

at low pressure,

     $\left(p+\frac{a}{V^{2}}\right)V=RT$

$pV+\frac{a}{V}=RT$

$pV=RT-\frac{a}{V}$

Divide both sid e by RT

        $\frac{pV}{RT}=1-\frac{a}{RTV}$