Question

Step 1

**Given information:**

Initial length of copper (L_{c}) = 20 cm = 0.2 m

Thermal expansion coefficient of copper (β_{c}) = 51 × 10^{-6}

Initial length of aluminium (L_{al}) = 30 cm = 0.3 m

Thermal expansion coefficient of aluminium (β_{al}) = 72 × 10^{-6}

Initial temperature of copper (T_{C(i)}) = 0^{0 }C

Initial temperature of aluminium (T_{AL(i)}) = 400^{0} C

Final temperature of both the metals (T_{C(f)}) =(T_{AL(f)}) = 205^{0} C

Step 2

The change in length for any change in temperature for a metal is given by the equation:

ΔL = L×ΔT×β

Where “L” is the initial length,

“ΔT” is change in temperature i.e. ΔT = (T_{f} - T_{i}),

“β” is coefficient of thermal expansion.

So, change in length for copper is given by substituting the corresponding value of copper:

ΔL_{(copper)} = 0.2 × (205 - 0) × (51 × 10^{-6}) = 0.2091 × 10^{-2} m = 0.2091 cm

Step 3

Change in length for aluminium is given by substituting the corresponding value of aluminium:

ΔL(aluminium) = 0.3 × (205 -400) × (72 × 1...

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