Assume the absolute zero apparatus is initially open to the air. The volume of a

Question

Assume the absolute zero apparatus is initially open to the air. The volume of a sphere is: V = 4r3/3 (radius=2inch)

a) Assume that air pressure is Po = 1.00 atm and the air temperature is To = 33degrees C. How many moles of air will the sphere hold? nair = ? moles

b) Suppose now that the apparatus, initially open, is now sealed with the air inside. If the apparatus is now heated to to 599 deg. C, find the pressure inside the apparatus now. P = ? atm

c) Assume now that, while maintaining a temperature of 599 deg. C, the sphere is injected with another 0.0357 moles of air. What is the new pressure inside the ball? P = ? atm

Explanation / Answer

radius = 2 inch or 0.0508 m

so,

volume = 4 * pi * 0.0508^3 / 3

volume = 0.0005491 m^3

1 atm = 101325 Pa

by gas equation

PV = nRT

101325 * 0.0005491 = n * 8.3145 * 306.15

nair = 0.0218573 moles

now the temperature is 599 degree

so,

P * 0.0005491 = 0.0218573 * 8.3145 * 872.15

P = 288650.55192 Pa or 2.8487 atm

if 0.0357 moles were injected

P * 0.0005491 = (0.0218573 + 0.0357) * 8.3145 * 872.15

P = 760109.73048 Pa or 7.5017 atm

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