A rigid, thermally insulated container is divided into two equal compartments by a thin partition. One compartment contains an ideal gas at an initial temperature \(T_i\), while the other compartment is evacuated. The partition is suddenly removed, allowing the gas to expand freely to fill the entire container. Which of the following correctly identifies the work \(W\) done ON the gas during the expansion, the relationship between the final temperature \(T_f\) and initial temperature \(T_i\), and the sign of the entropy change of the universe \(\Delta S_{\text{univ}}\)?