7. (Extra credit) A 10-m-high open cylinder, with Acyl = 0.1 m², contains 20°C water

above, and 2 kg of 20°C water below a 198.5-kg thin insulated floating piston, as shown

below. Assume standard g, Po, and liquid density of 1000 kg/m³. Now heat is added

to the water below the piston so that it expands, pushing the piston up, causing the

water on top to spill over the edge. This process continues until the piston reaches the

top of the cylinder.

(a) Find a relation for pressure as a function of volume.

(b) Find the initial pressure in the water below the piston.

(c) Find the final state of the water below the piston (T, P, v).

(d) Draw the process on a P-v diagram with lines of constant temperature./nPo

B₂C

H₂O

Figure 1: Schematic for Problem 7.