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:
[tex]pV_A = nRT[/tex]
where
[tex]p=1.01\cdot 10^5 Pa[/tex] is the gas pressure
VA is the gas volume
n is the number of moles of the gas
R is the gas constant
[tex]T=0^{\circ}C+273=273 K[/tex] is the gas temperature
So we can write the volume of the gas as
[tex]V_A=\frac{nRT}{p}[/tex]
Cylinder B contains glycering, so we can write its volume as
[tex]V_B=\frac{m_B}{\rho}[/tex]
where
mB is the mass of the glycerin
[tex]\rho = 1260 kg/m^3[/tex] 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,
[tex]V_A=4V_B[/tex]
Substituting the two expressions that we found previously, we get
[tex]\frac{nRT}{p}=4\frac{m_B}{\rho}[/tex]
Moreover, the number of moles of the gas can be rewritten as
[tex]n=\frac{m_A}{M}[/tex]
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:
[tex]\frac{m_ART}{Mp}=4\frac{m_B}{\rho}[/tex]
[tex]\frac{m_B}{m_A}=\frac{RT\rho}{4Mp}=\frac{(8.31)(273)(1260)}{4(1.01\cdot 10^5)(0.004)}=1769[/tex]
Learn more about ideal gases:
brainly.com/question/9321544
brainly.com/question/7316997
brainly.com/question/3658563
#LearnwithBrainly
