A 10.02 kg frictionless Piston with a cross sectional area of 0.001 m^2 is compr

Question

A 10.02 kg frictionless Piston with a cross sectional area of 0.001 m^2 is compressing 2.000 kg of H_2O in a steel cylinder. A. The initial temperature of the system is 300 degree C. a. What is the initial abs Pressure in the tank? b. What is the initial Volume of the tank? B. The gas is compressed isothermally until the volume is half of its original value a. how much heat gained (or lost) b. how much work done by (or on) the system c. what is the quality? C. At this point the piston becomes stuck and will not move up or down. Unable to compress the gas further due to the stuck piston, the cylinder is put in an ice bath at 32 F and cooled until the water in the cylinder reaches a temperature of 50 F. a. how much heat gained (or lost) b. how much work done by (or on) the system c. How quickly does the piston cool? (Ice bath temperature is constant) d. What is the quality when a temperature of 50 F is reached? e. Calculate the final pressure of the system at 50 F. D. Use the following page to make a detailed Sketch of this event on the H_2O PVT Diagram below for the above stats (initial, when piston sticks, and final after cylinder has been cooled)

Explanation / Answer

(A)(a) Pressure in the tank is due to the weight of the piston and due to atmospheric pressure
  Pressure due to weight = 10.02*9.81 / 0.001 = 98.296 kPa
and due to atmosphere = 101.325 kPa
Hence the net absolute pressure is = 98.296 + 101.325 = 199.62 kPa
(b) PV = mRT
  199.62*V = 2*(8.314/18)*(300+273)
V = 2.65 m3
(B) (a) In isothermal process heat interaction = work done
Work done = PVln(V2/V1) = 199.62*2.65ln(1/2) = -366.67 kJ
(b) Work done = -366.67 kJ

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