$1.(30$ points$)$ Classify the systems shown in the following figures. Each system is indicated by the dashed line. $($By classification, we mean answering the questions like: is it homogeneous$/$nonhomogeneous$?,$ is it closed or open?, is it adiabatic or not?, is it isolated or not?, does it have fixed or moving boundaries?$)$ Explain your reasons. Otherwise, you'll get partial credit.

a$)$ Closed tank that contains some liquid and some gas at the same temperature.

b$)$ Closed tank that contains some liquid and some gas at different temperatures. The tank is thermally insulated.

c$)$ Thermally insulated condenser of a laboratory$-$scale distillation unit. Hot vapor flows through the center of the condenser while cold water flows on the outside, causing the vapor to condense.