Question

A thin aluminium plate has an area 286 cm2

at 200C. Find its area when it is heated to 180
0C. ( of aluminium= 4.9 X 10-5
/
0C)​

Answer 1

Given:

Area of the aluminium plate (A₀) = 286 cm²

Initial temperature (T₁) = 20°C

Temperature at time t $(T_{2})$ = 180°C

Coefficient of Thermal expansion $(\alpha )$ = 4.9×10⁻⁵ /°C

To find:

Final area after thermal expansion ($A_{}$).

Explanation:

• The coefficient of thermal expansion (α) is the change in area of an object by unit length with change in temperature by a degree.

• The heat produced in the conductor could possibly result in expansion or change of area of the object.
• A very relatable example of expansion is the Expansion of rail tracks in summer, to avoid this, gaps are left between two adjoining rail tracks so that on expansion, the gaps could fill the extra area.
• Mathematically, it is given by

            $\alpha = \frac{(A - A_{0} )}{A_{0}(T-T_{0} ) }$

Solution:

According to the question, a thin aluminium plate of initial area A₀ = 286cm² at temperature T₁= 20°C  has expanded to area A with temperature T₂= 180°C.

Hence, substituting the given values in the equation, we get

$4.9*10^{-5} = \frac{(A-286)}{286(180-20)}$

$(A-286)= 4.9*10^{-5}*286(160)$

$A-286=2.24224$  $;$ $or$

$A=288.24 cm^{2}$

Final answer:

Hence, the area of the aluminium plate after expansion under thermal expansion with at 180°C will be 288.24 cm².