Answer:
(a) 106 kPa
(b) 0.0377 mol
(c) 17.8 cm
Explanation:
(a) There are three forces on the piston. Atmospheric pressure pushing down, weight pulling down, and pressure of the gas pushing up.
∑F = ma
PA − mg − PₐA = 0
P = (PₐA + mg) / A
P = Pₐ + (mg / A)
P = 101,300 Pa + (40.0 N) / (π (0.05 m²))
P = 106,393 Pa
P = 106 kPa
(b) Use ideal gas law.
PV = nRT
(106,393 Pa) (π (0.05 m²) (0.11 m)) = n (8.314 Pa m³/mol/K) (20 + 273.15) K
n = 0.0377 mol
(c) Use ideal gas law to find the new volume of the gas.
PV = nRT
(106,393 Pa) (π (0.05 m²) h) = (0.0377 mol) (8.314 Pa m³/mol/K) (200 + 273.15) K
h = 0.178 m
h = 17.8 cm
