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THERMAL EXPANSION PRACTICE PROBLEM AND ANSWER

 

1.     A rod of aluminum is 5 m at 200C. It is heated until 700C. The linear expansion coefficient of the aluminum is 0.000024/0C.  Calculate the length of aluminum at 700C!

Answer:

Given : α = 0.000024/0C

             ΔT = 700C – 200C= 500C

             L0 = 5 m

Find : Lt = …..?

Formula :

Lt = L0 ( 1 + α ΔT )

    = 5 m ( 1 + 0.000024/0C x 500C )

    = 5 m ( 1.0012 )

    = 5.006 m

2.     A plat of metal is 6.5 m2 at 100C. It is heated until 800C. The coefficient of linear expansion of the metal is 0.000011/0C. Calculate the area of the metal at 800C!

Answer:

Given : α = 0.000011/0C

             ΔT = 800C – 100C = 700C

             A0 = 6,5 m2

Find : At = …..?

Formula :

At = A0 ( 1 + 2α x ΔT)

     = 6.5 m2 ( 1 + 2 x 0.000011/0C x 700C )

     = 6.5 m2 ( 1.00154 )

     = 6.51001 m2

3.     A metal plate has size 15 cm x 30 cm at 250C. The coefficient of linear expansion of the plate is 0.00001/0C. Calculate its area at 750C!

Answer:

Given : α = 0.00001/0C

             ΔT = 750C – 250C = 500C

             A0 = 15 cm x 30 cm = 450 cm2

Find : At = …..?

Formula :

At = A0 ( 1 + 2α x ΔT)

     = 450 cm2 ( 1 + 2 x 0.00001/0C x 500C )

     = 450 cm2 ( 1.001 )

     = 450.45 cm2

4.     . A block of metal has a volume of 4.5 cm3 at 00 C. It is heated until 500 C. The coefficient of linear expansion of the metal is 0.000012/ 0C. Calculate the volume of the metal at 500C!

Answer :

Given : α = 0.000012/0C

             ΔT = 500C – 00C = 500C

             V0 = 4.5cm3

Find : Vt = …..?

Formula :

Vt = V0 ( 1 + 3α x ΔT)

     = 4.5 cm3 ( 1 + 3 x 0.000012/0C x 500C )

     = 4.5 cm3 ( 1.0018 )

     = 4.5081 cm3

5.     A block metal has side 25 cm x 20 cm x 40 cm at 100C. The coefficient of linear expansion of the metal is 0.000012/0C. Calculate its volume at 1100 C!

Answer:

Given : α = 0.000012/0C

             ΔT = 1100C – 100C = 1000C

             V0 = 25 cm x 20 cm x 40 cm = 20000 cm3

Find : Vt = …..?

Formula :

Vt = V0 ( 1 + 3α x ΔT)

     = 20000 cm3 ( 1 + 3 x 0.000012/0C x 1000C )

     = 20000 cm3 ( 1.0036 )

     = 20072 cm3

6.     The volume of water in a container is 250 L at 200 C. It is heated until 450 C. The coefficient of volume expansion of water is 0.00021/ 0C. Calculate the volume of the water at 450C. (Assume the container doesn’t expand)

Answer:

Given : γ = 0.00021/0C

             ΔT = 450C – 200C = 250C

             V0 = 250 L

Find : Vt = …..?

Formula :

Vt = V0 ( 1 +γ x ΔT)

     = 250L ( 1 + 0.00021/0C x 250C )

     = 250 L ( 1.00525 )

     = 251.3125 L

 

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