Serway & Jewett — Temperature: Problem 32

Why is the following situation impossible? An apparatus is designed so that steam initially at \( T = 150^\circ\text{C} \), \( P = 1.00\text{ atm} \), and \( V = 0.500\text{ m}^3 \) in a piston–cylinder apparatus undergoes a process in which (1) the volume remains constant and the pressure drops to \( 0.870\text{ atm} \), followed by (2) an expansion in which the pressure remains constant and the volume increases to \( 1.00\text{ m}^3 \), followed by (3) a return to the initial conditions. It is important that the pressure of the gas never fall below \( 0.850\text{ atm} \) so that the piston will support a delicate and very expensive part of the apparatus. Without such support, the delicate apparatus can be severely damaged and rendered useless. When the design is turned into a working prototype, it operates perfectly.