1 )
The length of a metallic rod is 5 m at 0 C ( Celsius ) and become 5.01 m on
heating up to heating up to 100 C . The linear expansion of metal will be : -
Solution
: -
L = L˳ ( 1 + α ∆ t )
. . . . . . . . eq. 1
∴ L = final length and L˳
= initial length .
∴ α = coefficient of linear expansion .
So , eq. 1 : -
5.01 = 5 ( 1 + α ∆ t ) ,
5.01 = 5 + 5 α ∆ t
,
0.01 = 5 α ( 100 – 0 ) ,
α = ( 10 ^ ( - 2) ) / ( 5
x 10 ^ 2 )
So , α
= 2 x 10 ^ ( - 5 ) / C ,
Answer .
. .
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2 )
A metal rod of silver at 0 C ( Celsius ) is heated to 100 C , its length is
increased to 0.19 cm . The coefficient of cubical expansion of the silver rod
is : -
Solution
: -
∆ L = L˳ α ∆ t
,
0.19 = L˳ α ∆ t
,
L˳ α = 0.19 / 100
= 1.9 x 10 ^ ( - 3 ) ,
Let , L˳ = 1 m .
So ,
α = 1.9 x 10 ^ ( - 3 ) , it is linear coefficient of expansion .
So ,
Volumetric ( cubical ) coefficient of expansion = 3 α = 5.7
x 10 ^ ( - 5 ) / C , Answer .
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