Ratio between mass of B and mass of A: 1769
Explanation:
Cylinder A is filled with helium gas. Assuming it is an ideal gas, we can write the equation:
where
is the gas pressure
VA is the gas volume
n is the number of moles of the gas
R is the gas constant
is the gas temperature
So we can write the volume of the gas as
Cylinder B contains glycering, so we can write its volume as
where
mB is the mass of the glycerin
is the density
We know that cylinder A and cylinder B have equal heights, but the diameter of cylinder B is half of that of cylinder A: since the volume of a cylinder is proportional to the square of the radius (therefore, to the square of the diameter), this means that cylinder A has a volume which is 4 times the volume of cylinder B. Therefore,
Substituting the two expressions that we found previously, we get
Moreover, the number of moles of the gas can be rewritten as
where
mA is the mass of helium
M = 4 g/mol = 0.004 kg/mol is the molar mass of helium
Substituting and re-arranging, we can find the ratio between the masses:
Learn more about ideal gases:
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