Question

Show that RTc/PcVc=8/3​

Answer 1

Please refer to the attachment for explanation...

Answer 2

Explanation :

The formula of compressibility factor at critical point is:

$Z=\frac{P_cV_c}{RT_c}$

As we know that:

The formula of Critical temperature is,

$T_c=\frac{8a}{27Rb}$

The formula of Critical pressure is,

$P_c=\frac{a}{27b^2}$

The formula of Critical volume is,

$V_c=3b$

Now put all the given values in the above formula, we get:

$\frac{P_cV_c}{RT_c}=\frac{(\frac{a}{27b^2})\times (3b)}{R\times (\frac{8a}{27Rb})}$

$\frac{P_cV_c}{RT_c}=\frac{3}{8}$

$\frac{RT_c}{P_cV_c}=\frac{8}{3}$

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