Consider a piston–cylinder assembly containing 10 kg of water. Initially the gas has a pressure of 20 bar and occupies a volume of 1.0 m3. Under these conditions, water does not behave as an ideal gas.

(a)    The system now undergoes a reversible process in which it is compressed to 100 bar. The pressure–volume relationship is given by

Pv1.5  5 constant

What is the final temperature and internal energy of the system? Sketch this process on a Pv diagram. Draw the area that represents the work for this process. Calculate the work done during this process. How much heat was exchanged?

(b)     Consider a different process by which the system gets to the same final state as in part (a). In this case, a large block is placed on the piston, forcing it to compress. Sketch this process on a Pv diagram. Draw the area that represents the work for this process. Calculate the work done during this process. How much heat was exchanged?

(c)     Can you think of a process by which the system could go from the initial state to the final state with no net heat exchange with the surroundings? Describe such a process, putting in numerical values wherever possible, and sketch it on a Pv diagram.