Provide the mathematical equation for entropy change.

In which case is the change in entropy negative?

In which of the following reactions,standard reaction entropy change $(\Delta S^o)$ is positive and standard Gibb's energy change $(\Delta G^o)$ decreases sharply with increasing temperature?

The entropy change in the isothermal reversible expansion of $2 \, \text{moles}$ of an ideal gas from $10 \, L$ to $100 \, L$ at $300 \, K$ is $..... \, J \, K^{-1}$.

The second law of thermodynamics states that in a cyclic process:

Direct conversion of $A$ to $B$ is difficult,so it is carried out by the path shown below. If $e.u.$ is the entropy unit,what will be $\Delta S_{(A \rightarrow B)}$?
Given:
$\Delta S_{(A \rightarrow C)} = 50 \ e.u.$
$\Delta S_{(C \rightarrow D)} = 30 \ e.u.$
$\Delta S_{(B \rightarrow D)} = 20 \ e.u.$