Calculate the work done if $1 \ mole$ of an ideal gas is compressed isothermally and reversibly from $12 \ dm^3$ to $6 \ dm^3$ at $300 \ K$. $\left[R = 8.314 \ J \ K^{-1} \ mol^{-1}\right]$ (in $kJ$)

At the transition temperature $T$, $\Delta G^0 = 0$ and $\Delta G^0 = 105 - 35 \log T$, where $A$ and $B$ are two states of substance $X$. The transition temperature in $^\circ\text{C}$ when pressure is $1 \text{ atm}$ is . . . . . . .

For a spontaneous process,which of the following conditions must be met?

$A$ process is taking place at constant temperature and pressure. Then

Compare the following criteria for spontaneity of a reaction based on the values of $\Delta_{\text{r}}H^0$,$\Delta_{\text{r}}S^0$,and $\Delta_{\text{r}}G^0$:

$\Delta_{\text{r}}H^0$	$\Delta_{\text{r}}S^0$	$\Delta_{\text{r}}G^0$	Description
$(a) (+)$	$(-)$	$(+)$	$(i) \text{ Non-spontaneous at all temperatures}$
$(b) (-)$	$(-)$	$(-)$	$(ii) \text{ Spontaneous at low temperatures}$
$(c) (-)$	$(+)$	$(-)$	$(iii) \text{ Spontaneous at all temperatures}$

The values of $\Delta H$ and $\Delta S$ for the reaction,$C_{(graphite)} + CO_{2(g)} \rightarrow 2CO_{(g)}$ are $170 \ kJ$ and $170 \ J \ K^{-1}$ respectively. This reaction will be spontaneous at temperatures greater than ............ $K$.