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Amiraneli [1.4K]
3 years ago
11

Planners of an experiment are evaluating the design of a sphere of radius r that is to be filled with helium (0°c, 1 atm pressur

e). ultrathin silver foil of thickness t will be used to make the sphere, and the designers claim that the mass of helium in the sphere will equal the mass of silver used. assuming that t is much less than r, calculate the ratio t/r for such a sphere.
Mathematics
1 answer:
Vikentia [17]3 years ago
6 0
The solution is:A mole of gas occupies 22.4 L A liter is 1000 cubic centimeters because 1 cubic centimeter = 1 mL
One Helium molecule (essentially one helium atom) has atomic mass 4 g/mol So for every 22400 cubic centimeters of volume, we have 4 grams of helium Density of helium = 4g / 22400 cm^3 = 1g / 5600 cm^3 
Volume of a sphere = (4/3)(pi)r^3 Volume of the outside sphere (the entire sphere) is (4/3)(pi)(R+T)^3 Volume of the inside sphere (the hollow region) is (4/3)(pi)R^3 
The difference for the volume of silver. (4/3)(pi)(R+T)^3 - (4/3)(pi)R^3 = (4/3)(pi)(3R^2T + 3RT^2 + T^3) 
The density of silver is 10.5g/cm^3 
So the mass of the silver is computed by:10.5*(4/3)(pi)(3R^2T + 3RT^2 + T^3) = (14*pi)(3R^2T + 3RT^2 + T^3) = (14pi)T(3R^2 + 3RT + T^2) 

Now for the mass of helium: volume x density = (4/3)(pi)R^3 (1/5600) = (pi/4200)R^3 

Set the two masses equal: (pi/4200)R^3 = (14pi)T(3R^2 + 3RT + T^2) R^3 = 58800*T(3R^2 + 3RT + T^2) R / T = 58800*(3R^2 + 3RT + T^2) / R^2 = 58800*( 3+T/R^2+(T/R)^2) 
then solve for xx = T / R 1/x = 58800*( 3+x/R+x^2) 1/58800 = x (3 + x/R + x^2) 1/58800 = 3x + x^3 x^3 + 3x - 1/58800= 0 x = ~ 5.66893x10^(-6)
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Answer:

x = 9, y = 27

Step-by-step explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

\frac{x-1}{6} = \frac{16}{12} ( cross- multiply )

12(x - 1) = 96 ( divide both sides by 12 )

x - 1 = 8 ( add 1 to both sides )

x = 9

Also

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3 years ago
3a+4b= c solve for b
Alina [70]

Answer:

b = (c - 3a)/4

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2 years ago
What is 3.8 repeating as a fraction in simplest form
Olin [163]
\bf 3.8888888\overline{8}\\\\
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3 years ago
Six notebooks cost $8.34. How much per notebook?
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3 years ago
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I need help solving number 17.
melisa1 [442]
Let x = amount of sales (in dollars)

The salary is $400 and there's an additional 0.06x dollars added on to get to the goal of 790. The equation is therefore

<span>400+0.06x = 790
</span>
Let's solve for x

400+0.06x = 790
<span>400+0.06x-400 = 790-400
</span>0.06x = 390
0.06x/0.06 = 390/0.06
x = 6500

The final answer is 6500

This means he must have $6,500 in sales. 
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3 years ago
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