Question

The relationship between $P_c,V_c$ and $T_c$ is:

• A. $P_c{V}_c=R{T}_c$
• B. $P_c{V}_c=3R{T}_c$
• C. $P_c{V}_c=\frac{3}{5}R{T}_c$
• D. $P_c{V}_c=\frac{3}{8}R{T}_c$

Answer 1

The correct option is D $P_c{V}_c=\frac{3}{8}R{T}_c$

$T_c=$ Temperature at and above which the vapour state can not be further liquified.

$P_c=$ Pressure of gas in its critical state

$V_c=$ Volume of gas in its critical state.

relation with the van der waals constants -

$T_c=8a/27Rb$ So $a=27T_{c}Rb/8$

$V_c=3b$ So $b=V_c/3$

$P_c=a/27b^2$ ....(1)

put the value of a and b in equation (1)

$P_c=\frac{27T_c\times R\times b}{8\times 27\times b^2}$

$P_c=\frac{27T_c.R}{8\times 27\times b}=\frac{27T_c.R}{8\times 27\times V_c/3}$

$P_c{V}_c=\frac{3}{8}R{T}_c$