Item 8 Part A A 22-cm-diameter vertical cylinder is sealed at the top by a frict

Question

Item 8 Part A A 22-cm-diameter vertical cylinder is sealed at the top by a frictionless 22 kg piston. The piston is 87 cm above the bottom when the gas temperature is 318 °C. The air above the piston is at 1.00 atm pressure What is the gas pressure inside the cylinder? Express your answer to four significant figures and include the appropriate units LA PoValue Units Submit My Answers Give Up Part B What will the height of the piston be if the temperature is lowered to 20 °C? Express your answer to two significant figures and include the appropriate units HA 1Value Units Submit My Answers Give Up

Explanation / Answer

a) P = F / A = (22 * 9.8) / (pi * 0.112) = 5671.7 Pa

Total pressure = 5671.7 + (1.013 * 105)

= 1.07 * 105 Pa

b) P V = n R T

V = pi * 0.112 * 0.87 = 0.0331 m3

n = 1.07 * 105 * 0.0331 / (8.314 * (318 + 273) ) = 0.721 moles

T = 20 + 273 = 293 K

V = 0.721 * 8.314 * 293 / 1.07 * 105 = 0.0164 m3

V = area * height

height h = 0.0164 / [pi * 0.112]

height h = 0.431 m

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