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:
![pV_A = nRT](https://tex.z-dn.net/?f=pV_A%20%3D%20nRT)
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
![V_A=\frac{nRT}{p}](https://tex.z-dn.net/?f=V_A%3D%5Cfrac%7BnRT%7D%7Bp%7D)
Cylinder B contains glycering, so we can write its volume as
![V_B=\frac{m_B}{\rho}](https://tex.z-dn.net/?f=V_B%3D%5Cfrac%7Bm_B%7D%7B%5Crho%7D)
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,
![V_A=4V_B](https://tex.z-dn.net/?f=V_A%3D4V_B)
Substituting the two expressions that we found previously, we get
![\frac{nRT}{p}=4\frac{m_B}{\rho}](https://tex.z-dn.net/?f=%5Cfrac%7BnRT%7D%7Bp%7D%3D4%5Cfrac%7Bm_B%7D%7B%5Crho%7D)
Moreover, the number of moles of the gas can be rewritten as
![n=\frac{m_A}{M}](https://tex.z-dn.net/?f=n%3D%5Cfrac%7Bm_A%7D%7BM%7D)
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:
![\frac{m_ART}{Mp}=4\frac{m_B}{\rho}](https://tex.z-dn.net/?f=%5Cfrac%7Bm_ART%7D%7BMp%7D%3D4%5Cfrac%7Bm_B%7D%7B%5Crho%7D)
![\frac{m_B}{m_A}=\frac{RT\rho}{4Mp}=\frac{(8.31)(273)(1260)}{4(1.01\cdot 10^5)(0.004)}=1769](https://tex.z-dn.net/?f=%5Cfrac%7Bm_B%7D%7Bm_A%7D%3D%5Cfrac%7BRT%5Crho%7D%7B4Mp%7D%3D%5Cfrac%7B%288.31%29%28273%29%281260%29%7D%7B4%281.01%5Ccdot%2010%5E5%29%280.004%29%7D%3D1769)
Learn more about ideal gases:
brainly.com/question/9321544
brainly.com/question/7316997
brainly.com/question/3658563
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