1) The length of a metallic rod is 5 m at 0 C ( Celsius ) and become 5.01m on heating up to heating up to 100 C . The linear expansion of metal will be ?

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 .

 

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

 

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 .

 

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .