Question
Download Solution PDFSaturated water vapor at 200 kPa is in a constant-pressure cylinder/piston assembly. At this state, the piston is 0.1 m above from the cylinder bottom (as shown). What will be the distance of the piston from bottom if temperature is raised to 200°C
[Given: For P = 200 kPa: Tsat = 120.23°C, specific volume of saturated liquid water (vf) = 0.001 m3/kg, specific volume of saturated water vapor (vg) = 0.88 m3/kg; specific volume of superheated water vapor at 200°C and 200 kPa is. v = 1.1 m3/kg]
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
In a constant-pressure piston-cylinder system, the height of the piston is directly proportional to the specific volume of the vapor, since volume = area × height and area remains constant.
So, we use the relation: \( \frac{h_1}{h_2} = \frac{v_1}{v_2} \Rightarrow h_2 = h_1 \times \frac{v_2}{v_1} \)
Calculation:
Given:
Initial specific volume, \(v_1 = 0.88~m^3/kg\)
Final specific volume, \(v_2 = 1.1~m^3/kg\)
Initial height of piston, \(h_1 = 0.1~m\)
Using relation,
\(h_2 = 0.1 \times \frac{1.1}{0.88} = 0.1 \times 1.25 = 0.125~m\)
Final distance of piston from cylinder bottom: 0.125 m
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