Question

A frictionless piston/cylinder apparatus 100 mm in diameter contains water vapor with a quality of 20%. The piston, which has a mass of 16 kg, is floating on the vapor 50 mm above the bottom of the cylinder. Stops above the piston prevent it from moving upward more than 30 mm. Heat is added until the temperature reaches 400?C. Find: a. the initial pressure b. the mass of water c. the quality when the piston hits the stops d. the final pressure of the water e. the work done by the water.

Answer 1

Initial pressure, P = F/A = 16 times 9.81/pi/4 times (0.1)^2 = 19.984 Kpa = 20 Kpa Initial pressure, p initial = p + P_atm = 20 + 101.325 = 121.325 kpa specific volume, v_1 = vf + x(vg - vf) = 0.001 + 0.2(1.4188 - 0.001) = 0.28456 m^3/kg mass of water, m = pi/4 times (0.1)^2 times 50/1000/0.28456 = 0.00138 kg volume of state 2, v_2 = pi/4 times (0.1)^2 times 80/1000\r\n = 6.283 times 10^- 4 m^3 v_2 = 6.283 times 10^- 4/0.00138 = 0.45528 m^3/kg because v < vg therefore v = vf + x(vfg) 0.45528 = 0.001 + x(1.4188 - 0.001) therefore x = 0.32 at v = 0.45528 m^3/kg & T = 400 degree C p = 676.3 kpa = 0.67 mpa therefore workdone, w = integral^1_1 pdv = p(v_2 - v_1) = 121(6.283 times 10^- 4 - 3.927 times 10^- 4