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 : L_t = …..?

Formula :

L_t = 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 : A_t = …..?

Formula :

A_t = 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 : A_t = …..?

Formula :

A_t = 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 : V_t = …..?

Formula :

V_t = 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 : V_t = …..?

Formula :

V_t = 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 : V_t = …..?

Formula :

V_t = V₀ ( 1 +γ x ΔT)

     = 250L ( 1 + 0.00021/⁰C x 25⁰C )

     = 250 L ( 1.00525 )

     = 251.3125 L