An irreversible process occurring isothermally in an isolated system leads to

Provide the mathematical equation for entropy change.

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:
$\Delta S_{(A \rightarrow C)} = 50 \ e.u.$
$\Delta S_{(C \rightarrow D)} = 30 \ e.u.$
$\Delta S_{(B \rightarrow D)} = 20 \ e.u.$

When disorder of a system increases,the change is said to be

Which of the following statements is true? The entropy of the universe

One mole of an ideal gas is expanded isothermally and reversibly to half of its initial pressure. $\Delta S$ for the process in $J \ K^{-1} \ mol^{-1}$ is $[\ln \ 2 = 0.693$ and $R = 8.314 \ J \ mol^{-1} \ K^{-1}]$