A vessel initially contains 1000 kg of saturated liquid water at T = 30°C, which needs to be cooled. The vessel is adiabatic but has a piston that allows pressure and volume to be changed and a valve that can be opened to allow vapor to escape through the top. So, a small portion of the water is allowed to evaporate and escape, resulting in the cooling of the remaining water. Calculate each of the following, and state and justify any assumptions that you make.

A. The temperature of the water remaining in the vessel if 1 kg of water evaporated.

B. The amount of water that would have to evaporate in order to cool the water remaining in the vessel to 25°C.

C. The amount of water that would have to evaporate in order to cool the water remaining in the vessel to 20°C.