Question
1. A structural I beam is made of iron. A view of its cross-section and its...
1. A structural I beam is made of iron. A view of its cross-section and its dimensions is shown in the figure, where d = 2 cm, w = 29 cm, h = 30 cm and the length (not shown) of the beam is l = 1.29 m. The density of iron is 7560 kg/m3 . The atomic weight of iron is 55.85 g/mol and Avo- gadro number is NA = 6.02214x10^23 /mol.
2. How many atoms are there in this section? Answer in units of atoms.
Answers
dividing the cross section into 3 parts as shown
the area of cross section = areas of part1 + part2 +part 3
= (w*d)+((h-2d)(d))+(w*d)
= 2(29*2)+( 26*2)
= 168cm2
the area of cross section = 168cm2
the volue of I beam = area * length
= 168*129
= 21672 cm3
= 2.167*10-2 m3
the volue of I beam = 2.167*10-2 m3
we know
density = mass/volume
mass = density*volume
= 7560 * 2.167*10-2
= 163.84kg
mass of beam = 163.84kg
no of moles of iron = mass of beam /atomic weight
= 163.84*103/55.85
= 2.934 *103moles
no of moles of iron =2.934*103 moles
no of atoms = no of moles * NA
= 2.934*103*6.023*1023
= 1.767*1027 atoms
1.767*1027 atoms are there in the section
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