Question

The incorrect statements among the following is/are

• A. $\Delta S_{surrounding}$ at the boiling point of water is negative
• B. For a free expansion under adiabatic condition $PV$ is constant
• C. For an isothermal expansion,
  $\Delta S=nRln\left(\frac{V_2}{V_1}\right)$
• D. For a process to be spontaneous only at high temperature,
  
  $\Delta H$ and $\Delta S$ are negative

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\Delta S_{surrounding}$ at the boiling point of water is negative
B For a free expansion under adiabatic condition $PV$ is constant
C For an isothermal expansion,

$\Delta S=nRln\left(\frac{V_2}{V_1}\right)$
A) At Boiling point,
$\Delta H=-T\Delta S_{surrounding}$
since $\Delta H$ is positive, $\Delta S_{surrounding}$ must be negative.
B) For a free expansion of an ideal gas $w=0$
For an adiabatic expansion $q=0$
$\Delta U=0$. This implies $\Delta T=0$
So, for isothermal process according to Boyle's law $PV=constant$

C) For an isothermal expansion,
$\Delta G=-w=nRTln\left(\frac{V_2}{V_1}\right)=-T\Delta S$
$\Delta S=nRln\left(\frac{V_2}{V_1}\right)$

D) For a process to be spontaneous at high temperature,
Both $\Delta H$ and $\Delta S$ are positive. Example : Boiling of water occurs at high temperature since for which $\Delta H$ and $\Delta S$ are positive.