1. A washer is a ring of inner diameter 0.500 cm and outer diameter 0.750 cm at
ID: 1563214 • Letter: 1
Question
1. A washer is a ring of inner diameter 0.500 cm and outer diameter 0.750 cm at room temperature, made of aluminum. At what temperature will the ring pass over a bolt of outer diameter 0.501 cm? (The bolt is not heated).
2. A brass bar is one millimeter shorter than an iron bar of length exactly one meter at room temperature. At what temperature will they be equally long? (Both are heated, equally).
3. A 300 mL Pyrex glass is full of boiling water, at 100OC. If the volume coefficient of water is 102 x10-6 1/OC, find how much water could be added to the glass at room temperature if: (a) the Pyrex does not expand at all, and (b) considering the contraction of Pyrex.
Explanation / Answer
1) The area of the washer should be greater than the area of the bolt for the washer to pass.
A/Ao = 2 x expansion co efficient × T
Initial Area of the ring should be Ao = ( ( inner radius^2)
= 3.14 ×(0.0025^2) m^2
=1.96e-5 m^2
Area of the bolt = (r^2) =×(0.00251^2) =1.98e-5 m^2
A= 0.02e-5m^2
A/Ao = 0.02e-5 m^2/(1.98e-5) m^2 = 2× 23.1e-6/K × T
T = 218.6K
T-293K =511K ( room temperature = 293K)
T= 75 K
2)given at T=293 K
Lb =0.999m
Li=1m
At one temperature Lb ' = Li' ( both lengths are equal)
Lb + Lb = Li + Li
Lb + 2aLbT = Li + 2a' Li T (a,a' - linear expansion co effiecients)
T×2(aLb-a'Li) = Li-Lb
T = Li-Lb/2(aLb-a'Li)
=( 1-0.999)m/(2((19e-6×0.999)-(12e-6)))
=71.6 K
T-293 = 71.6
T = 365.6 K
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