100 POINTS. PLEASE EXPLAIN

(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

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