Question

Which of the following statement(s) is/are true:
I - Slope of isotherm at critical point is maximum.
II - Larger the value of $T_c$, easier is the liquefaction of gas.
III - van der Waals' equation of state is applicable below critical temperature at all pressures.

• A. Only I
• B. I & II
• C. II & III
• D. Only II

Answer 1

The correct option is B I & II

I - Slope of isotherm below critical point $<0$.
Slope of isotherm above critical point $<0$.
but slope of isotherm at critical point $=0$.
So slope of isotherm at critical point is maximum.
II. As $T_c=\frac{8a}{27Rb}$ $\Rightarrow T_c\propto \left(a/b\right)$
Larger value of $T_c$ means less decrease in temperature is required to liquefy the gas. So, easier will be the liquefaction.
III. When a gas is below the critical temperature, it is a 'liquid' so van der Waals equation of state in not valid.
Hence, the correct answer is option (b).