Question

A 30-cm-diameter vertical cylinder is sealed at the top by a frictionless 16 kg piston. The piston is 77 cm above the bottom when the gas temperature is304 ∘C. The air above the piston is at 1.00 atm pressure.

A) What is the gas pressure inside the cylinder?

B) What will the height of the piston be if the temperature is lowered to18 ∘C?

Answer 1

a )

using pressure P is

F = P X A

then P =F/A

P = 16 X 9.8 / 3.14 X 0.15²

P = 2219.39 pa

1 atmosphere = 1.013 X 10⁵ pa

total pressure is = 1.013 X 10⁵ + 2219.39

P = 103519.39 pa

b )

using P X V = n X R X T

we have the above values the P = 103519.39 pa

Volume = Area X height

V = 3.14 X 0.15² X 0.77 = 0.054 m³

R = 8.314 m³ Pa K⁻¹ mol⁻¹

T = 304 C = 304 + 273 = 577K

103519.39 X 0.0544 = n X 8.314 X 577

n = 5631.45 / 4797.178

n = 1.17 moles

P = 103519.39 Pa

T = 18 + 273 = 291K

R = 8.3145

103519.39 X V = 1.17 X 8.314 X 291

V = 2830.66 / 103519.39

V = 0.0273 m³

V = area X height

0.0273 = 3.14 X 0.15² X h

h = 0.0273 / 0.07065

h = 0.38 m