For $2 \ mol$ of $He$ (ideal gas),find the work done in a process where it is heated from $200 \ K$ to $400 \ K$ such that the enthalpy of the gas varies as : $H = 10 \ V^2$ (in $R$)

When is a reaction spontaneous?

At a temperature of $25^\circ C$,if $\Delta H < T \Delta S$,then $\Delta G$ = ?

For a reaction,$4 M (s) + n O_2 (g) \rightarrow 2 M_2 O_n (s)$,the free energy change is plotted as a function of temperature. The temperature below which the oxide is stable could be inferred from the plot as the point at which :

In the conversion of limestone to lime,$CaCO_{3(s)} \rightarrow CaO_{(s)} + CO_{2(g)}$,the values of $\Delta H^{\circ}$ and $\Delta S^{\circ}$ are $+179.1 \ kJ \ mol^{-1}$ and $160.2 \ J \ K^{-1} \ mol^{-1}$ respectively at $298 \ K$ and $1 \ bar$. Assuming that $\Delta H^{\circ}$ and $\Delta S^{\circ}$ do not change with temperature,the temperature above which the conversion of limestone to lime will be spontaneous is ........... $K$.

Identify the correct statement for the change in Gibbs energy $(\Delta G_{\text{system}})$ for a system at constant temperature and pressure.