Air is located in a piston-cylinder device. The diameter of the cylinder is 12 cm, the mass of the piston is 5 kg, and the acceleration due to gravity is 9.80 m/s2. The local atmospheric pressure is 100.5 kPa. Determine the mass of a set of weights that needs to be added to the top of the piston so that the absolute pressure of the air in the cylinder is 250 kPa.
Given: D = 12 cm = 0.12 m; m = 5 kg; g = 9.80 m/s2; Patm = 100.5 kPa; P = 250 kPa
What will be an ideal response?
The final gage pressure in the tank is Pg = P – Patm = 149.5 kPa = 149,500 Pa
The weight of the piston gives a gage pressure of
Pg = W/A = mg/(?D2/4) = 4,333 Pa
The added weights must supply a Pg,w = 149,500 Pa – 4,333 Pa = 145,167 Pa
To get this, we must add
m = (?D2/4)Pg,w / g = 168 kg
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