Question

What is the change in area (in cm²) of a 60.0 cm by 150 cm car windshield when the
temperature changes from 0 ℃ to 36 ℃? (The coefficient of linear expansion of glass is
9 x 10⁻⁶ ℃⁻¹).

Answer 1

Explanation:

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Answer 2

Answer:

The change in the area of the windshield is 5.832cm².

Explanation:

We will use the given relation to solve this question,

$\Delta A=A\beta \Delta T$        (1)

Where,

ΔA=change in area of the windshield

A=initial area of the windshield

β=coefficient of areal expansion

ΔT=change in temperature

From the question we have,

l₁=60 cm

l₂=150cm

T₁=0°C

T₂=36°C

α=9×10⁻⁶°C⁻¹

Also, the coefficient of the areal expansion is two times the coefficient of the linear expansion. So,

$\beta=2\alpha$      

$\beta=2\times 9\times 10^-^6=18\times 10^-^6$           (2)

And,

$\Delta T=T_2-T_1$

$\Delta T=36\textdegree-0\textdegree=36\textdegree C$        (3)

The initial area "A" is calculated as,

$A=l_1\times l_2$

$A=60\times 150=9000cm^2$   (4)

By substituting the required values in equation (1) we get;

$\Delta A=9000\times 18\times 10^-^6\times 36$

$\Delta A=5832\times 10^-^3$

$\Delta A=5.832 cm^2$

Hence, the change in the area of the windshield is 5.832cm².