Assume the absolute zero apparatus is initially open to the air. a) Assume that

Question

Assume the absolute zero apparatus is initially open to the air.

a) Assume that air pressure is Po = 1.00 atm and the air temperature is To = 16.4o C. How many moles of air will the sphere hold?
nair =   moles

b) Suppose now that the apparatus, initially open, is sealed with the air inside. If the apparatus is now heated to to 685o C, find the pressure inside the apparatus now.
P =  Pa

c) Assume now that the sphere is injected with another 0.0392 moles of air, and the temperature (685o C) is maintained. What is the new pressure inside the ball?
P =  Pa

Explanation / Answer

Taking radius of sphere = r = 2 m

so volume of sphere V = (4/3) *pi*r^3 = (4/3) *3.14 * (2^3) = 33.49333 m^3 = 33493.33 L

a)

T =16.4 C = 16.4 + 273 = 289.4 K

we have ideal gas law

PV = nRT

so 1 * 33493.33 = n * 0.0821 * 289.4

n = 1409.66736 moles

so nair =  1409.66736  moles

b)

T2 = 685 C = 685 + 273 = 958 K

we have P1/T1 = P2/T2

so 1/289.4 = P2/ 958

P2 = 3.310297 atm

pressure inside the apparatus now. = 335415.86 Pa

c)

number of moles = 0.0392 + 1409.66736 = 1409.70656 moles

so PV = nRT

P *  33493.33 = 1409.70656 *0.0821 * 958

P = 3.3103892 atm = 335425.18723 Pa

new pressure inside the ball = 335425.18723 Pa

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