19.0.0: LINEAR EXPANSION

19.1.0:   EXPANSION:
Expansion is the increase in the size of an object when the object is heated.
19.1.1:   EFFECT OF EXPANSION:

• Expansion causes sagging of transmission line

• Expansion cause bridge to bend

• Expansion causes glass cup to crack

19.1.2:   APPLICATION OF EXPANSION:
The idea of expansion is used in the following:

• Construction of bridges

• Construction of thermostat in electric iron and fridge.

• Is used in the design of some special alloy

19.2.0:   EXPANSIVITY
Expansivity is the increase in the length of a substance when its temperature increases by one kelvin or degree Celsius.

19.3.0:   LINEAR EXPANSIVITY
Linear expansivity is the increase in the length of a substance per unit length of the substance for one degree Celsius rise in temperature. The unit of linear expansivity is per Kelvin ( K𒐊−¹) or per degree Celsius ( ०C−¹ )
19.2.2:   FORMULA FOR CALCULATING LINEAR EXPANSIVITY
Linear expansivity = change in length / (initial length * temperature change )
Linear expansivity ∝= increase in length / (  L₁* ∆θ )
Linear expansivity ∝=  ( Lℤ₂ - L₁ ) / (  L₁* ∆θ )   ∝=  ( Lℤ₂ - L₁ ) / (  L₁* ∆θ )                                   ∝* (  L₁* ∆θ )  =   Lℤ₂ - L₁   ( cross and multiply )                                   ∝L₁∆θ = Lℤ₂ - L₁                                   ∝L₁∆θ + L₁ = Lℤ₂          ( collect like terms together)                                    L₁ (∝∆θ + 1 ) =  Lℤ₂     ( factorize L₁ )                                    (∝∆θ + 1 ) = Lℤ₂ /  L₁

Linear expansivity ∝= ( Lℤ₂ - L₁ ) / ( L₁* θ₂ - θ₁  )                                   ∝= ( Lℤ₂ - L₁ ) / ( L₁* θ₂ - θ₁  )   ∆θ    =    θ₂ - θ₁ which is called temperature change
  ∆L = Lℤ₂ - L₁ is called change in length or increase in length.
  Lℤ₂ is the final length of the substance at temperature  θ₂   L₁ is the initial length of the substance at temperature  θ₁  θ₁  is the initial temperature of the substance at length L₁  θ₂ is temperature of the substance at length Lℤ₂

EXAMPLES:

1. A metal rod has a length of 100cm at 200'C. At what temp. will its length be 99.4cm if the linear expansivity of the material of the rod is 0.00002/K? 

SOLUTION:

Data given in the question:Initial length L₁ = 100 cm Final lenght L₂ = 99.4 cm Initial temperature  θ₁ = 200°CFinal temperature  θ₂ = ?∝ =  0.00002/K
Formula:    Linear expansivity ∝= ( Lℤ₂ - L₁ ) / ( L₁* (θ₂ - θ₁ ) )
Substitution:   0.00002 = ( 99.4 - 100) / ( 100 * (θ₂ -  200 )

0.00002 =  - 0.6 / (100 θ₂ -  20000 )

0.00002. (100θ₂ -  20000 )   = - 0.6.   ( open the brackets ) 

         0.002 θ₂ + 0.4 = 0.60.002θ₂ =  - 0.6 - 0.4 θ₂= 0.2 / 0.002.       ➡      θ₂ = 100°C

2.