A perfectly insulated cylinder fitted with a leak-proof frictionless piston with a mass of 30.0 kg and a face area of 400 cm^2 contains 7.0 kg of liquid water and a 3.0 kg -bar of aluminum. The aluminum bar has an electrical coil imbedded in it, so that known amounts of heat can be transferred to it. Aluminum has a specific gravity of 2.70 and a specific internal energy given by the formulaU (kJ/kg)=0.94T(C). The internal energy of the liquid water at any temperature may be taken to be that of the saturated liquid at that temperature. Negligible heat is transferred to the cylinder wall. Atmospheric pressure is 1.00 atm. The cylinder and its contents are initially at 20 C. Suppose that 3310kJ is transferred to the bar from the heating coil and the contents of the cylinder are allowed to equilibrate.
a. What is the total pressure (in bar) exerted on the contents of the cylinder? What is the saturation temperature of the system? What is the specific internal energy and specific volume of saturated liquid water and steam for the final state of the system?
b. Is the amount of heat transferred to the sufficient to vaporize some of the water (meaning is the heat supplied more than the heat needed to heat the liqu id and the aluminum bar from 20C to the saturation temperature)? Explain.
c. What are the water mass balance equation and simplified energy balance equation for this
system? State all assumptions made.
d. What is the expansion work (W = PxV) done by the piston? (Hint: This will be in terms of mL and mv.)
e. Solve the water balance and simplified energy balance equations to determine the
volumes (in L) of liquid water and steam?
f. What is the piston displacement dz (in cm) from the initial state to the final state?